{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "56686640",
   "metadata": {},
   "source": [
    "# 项目6.微分积分RLC震荡\n",
    "\n",
    "- 姓名：马梓荃\n",
    "- 学号：20201060339\n",
    "- 邮箱：979324173@qq.com"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0eba98b",
   "metadata": {},
   "source": [
    "<a href=\"https://sm.ms/image/N38KqQHnMT9SOwu\" target=\"_blank\"><img src=\"https://s2.loli.net/2022/05/27/N38KqQHnMT9SOwu.jpg\" ></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24f26b44",
   "metadata": {},
   "source": [
    "## 项目介绍\n",
    "\n",
    "<a href=\"https://sm.ms/image/FSeZ8MlPcJvQbaE\" target=\"_blank\"><img src=\"https://s2.loli.net/2022/05/27/FSeZ8MlPcJvQbaE.jpg\" ></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85af158c",
   "metadata": {},
   "source": [
    "RLC电路是一种由电阻R、电感L、电容C组成的电路结构。RLC电路的组成结构一般有两种：串联型，并联型。作用有电子谐波振荡器、带通或带阻滤波器。\n",
    "本项目基于RLC电路，研究在欠阻尼条件下电路的震荡过程。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62e0b4d4",
   "metadata": {},
   "source": [
    "## 项目目的\n",
    "本项目需要分别利用微分和积分方法对震荡过程进行拟合。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "733e9cdf",
   "metadata": {},
   "source": [
    "### 1.准备工作"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "23da9a85",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "de558ee1",
   "metadata": {},
   "outputs": [],
   "source": [
    "R = 0.01\n",
    "L = 0.01\n",
    "C = 1e-5\n",
    "E = 12\n",
    "d = (4 * L / C - R ** 2) ** (1 / 2)\n",
    "c1 = d / (2 * L)\n",
    "c2 = - R / (2 * L)\n",
    "c3 = 2 * E / d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ff922a9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.arange(0,6,0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ced1acee",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(a):\n",
    "    return 2 * E * np.sin( d * a / 2 / L) * np.exp(- R * a / 2 / L) / d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7c9e92c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x171e4870c40>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,f(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6179771a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def di(t):\n",
    "    return 2*E*(1/d)*(c1*np.cos(c1*t)*np.exp(c2*t) + c2*np.sin(c1*t)*np.exp(c2*t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "78185deb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def si(t):\n",
    "    return c3*(np.exp(c2*t))*(-c1*np.cos(c1*t)+c2*np.sin(c1*t))/(c1**2+c2**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9af28a05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x171e501d820>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,di(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ad11088b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x171e508c700>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TksqVqnS7u1ygeYilpbDky41RMMZziVpVNjbQxab+LuoazixGy9HM5sp84juHmJaJzIKw7iQ68SRa6/twxKP52CeabmvgLltb9/g08CYfmw8DH245lgNuiHrtnaRcra8oNTakEjGrWWHeobAYZxZWFwrLphJU65pyrf15W1lsGrkPy/tcbD2W+UKFsX5nnEtfxhEW25EwWmtOzRe57eoMY/0ZAE7NF9jsjoex4ZPfO8zHv32IJ47N8YlfXtd/BoJw0SOd9x2k5JF8B6dKLMxj0VpT9vJYLENhZgJyJrGyQRIgbzE6P9cmLGafi12OZr6wnGPp73JsF4p2ojSTK1Ou1hnrzzA2YISlaGVruO+pUwD84OCUhNEEYZ0RYekgjmfg7bGECUvJo6IMoifvm4dYmknJNl5H8y4XWBYWG1utNXP5CgNmHExEj8U0U470ZtjU5wjL6QjCsliscHQ6z+WjPSyWqhyYkOS/IKwnIiwdpFytr0jcG1KJWGhVWMmjBwZcj8VGWBo5lqY+lghex1Kp1jgflr0dmxxLrlyjWteNHEuvKyyLth6L20y5oSdFXyZJTEUb2f/8mSUAfvIlmwF4QSYrC8K6IsLSQbz6UACr5L3JwaSTK3MhmWTceuQ+rOxjMd6LTff9UtHpQzF0RxCW+abmSOeaYyTjyrpzfyrnCkt3ilhMMZhNMZO379w/OOEIy61XjwLwwmR0YSlWasxFeE1BEPwRYekgvsJiEQrz6toH50O6XKuHzs/ySt43NlBarkU2CXuAnpQJhYXbmg/k/q4U4FTC9WWS1qEwMw5mqNuxH8gmI33In5groBRcOtzD5v5MZI9loVjhNX/4T9z2R9+1niQtCII/IiwdpFLzrwpbbSjMVHOFeS0med9sH0VYlkpVetLJxn2z2tjKY3HDViYUBs7Y/SjJ+5iCgawjLEPdKWZy9sJyar7AcE+aVCLGlsEuTkTcXvlP+88wuVhiYqHUKAIQBGH1iLB0kHLNPxRWCulFMY+3lgWnG2P3g8WhWK27WyOXJ940NlCWg1+7XtfkylV6mjyWZDxGKhGzEhYzJ2yFsGQSLEYIhQ1mU8Rjyn2eVKQcy8m5YqM0eVN/FxML0SrKvvvcFIPZJD3pBI8enY1kKwhCOyIsHaTkk7xPJ+OUQj2Wdo8D7LdIFlt2scCyxxJWrpyv1NCaFcl7cBL4NlVhJsdiqsHASeDbhsKax8EADGWjeSwn5wtsdsuUN/WlOTVfjDSn7MDEAtds6edl2/p5cnw+3EAQhEBEWDrI2pL3fqEwO4+lUK6t6GGBZVEKE5ZcywBKg+ncD8PLvq8rYR0KWyhWGpVkAAPdSebyFWtxmFwoMdLrCkt/F6Vq3brrv17XHDyzxOWjvVw11sdzE4uR98Ecn8nzX//xgLWHJggXOh3pvBccvBocwTRIBn9AN4Ql6e2xhOZYqvUVPSywHAorhoiD8UrMGBdDd8rOYzHik23ymKIk75dKVfqaRGkom6Jcq5Mr11Y0bXpRrNRYLFUZ7nXmkzX6YBaKjZxNECfmChQrdXaP9FB1h25OLBYbUwRs+K2/fYK9R2eZWCjyh+94mbWdIFyoiMfSQXxzLBbJ++WqMO8cS1gCvui1y8W9H+axNEqVW4Spx3Lsfq5UJZ2IrZiR1teVtO5jWSxW6W0SlkFXEGYtwmHTTaXKsFxZNmO5aOz4bB5wVirv3NANwNHpvJUtwORiib1uXubr+yak618QEGHpKJWaT4NklD6W1lBY0m46sleOJRGPkYrHwoXFfTzbIiy2+1ycxP9Kz6I3naBQqVkN31wsVlbYD7riMGtRcjzlDqs0E5U39LjCYlmufHLOSfRvHuhix4YsAEen7cuVHzw8DcCdr72E+UKFZ09J178giLB0kKAhlKHC4lMVlrEsGS5WaiuaI5ftY6Gd+41QVpvHErcLhZVqjfJkQ1+X6b4PD4ctFasrciyDbiJ/1qIybMqsRHYFxXg7tsn/E7NOafLYQIbRvuhzyp45tUAyrvi5G7cCywvLbKnVNZ/4ziG+feBM+MmCcJ4gwtJBghokwzwOv1lhjeR9aFVYfcU4F0NXKnwD5fIul5Xi0J1KkLNokFwqVdvyM33uIMqwcFitrsmVaytDYd0RQmFuyMt4LEaUbIXl5FyB4d406UScVCLGhu5UpJH9z08ssmtjN5ds7KE7FeeZiMLy94+f4CNf2897P/MIJyP23wjCuYoISwfxExab6cZh5cZhwlTwCIWB3aKwQsX58M+2Ju8tQ2H5cq3N2+l1my3DxrosFVduroSmHItFOGuu4JxjemgS8RgD2aS1sEwtlRhxE/8Aw71pzizYC8tzE0vsHu0lFlNcOtLD4Yhd/196/ETj7/zLT7QuXhWE8xMRlg5SCkjeV+s6sIzVryosSvLeOxQWPsQy7zFnDNxy40r4orBcudreA+N6IEshHstiqb0HxlSI2ZQMzxcqxGNqhTBF6YOZyZcbCX+Akb4MZxbtQmHVWp0TcwV2uUn/rYNdnJi1T/yXqjUeOTLDL7x8O7tHehr5mihUa3WOz9i/piC8GIiwdIjGPhWfHAsE7733WmsMEcqNK/W2AZbghMJWWxWWTdntvc95hMJsVxubUFlzKCwRj9GTTrBQsOj6zzsrkZsnDkQZCTPrdv0bRiN4LKfmi9Tqmq2DTmnyloEuxmcL1v03z08sUarWuXHHEDftGuKxo7ORGju11rznMw/zmj/8J776pIyiEc4dRFg6RNX1RvwaJCFYHErVGomYWlGyC9E8Fs8cS9I+x9JWFdYYCRPWYNmevI8qLK3NmX2ZhLXHYqYqGwYjCMtMrtVjSTO5VKJm0SQ57ib+tw051WRbB7OUqnWmLEudD006U5kvG+nhyrE+FktVTkYoHNh7dJYfHHS8nP/5reet7QThbCPC0iHKPsl3WBaHoDxLqeLXXGnrsXiHwuxyLI6otVa0ZS3H7uc9yo0bobAQYVlyQ2HNVWFghliuTlg2WApLpVZnoVhd4bGM9Gao1bWV/bgb9toy0LXit+0QzMOTOZSCHRuy7NnUC8CB0/bJ/28+O0Eyrvi3t+9h/+nFVe2hefrEPHmLtQqCEAURlg5hRMOv3BiCQ2FBa42dx/3FoVKrU61rz+R9JmWXY2kNg8FyMt/KY+lgKAxcYVmlxzLUnWI2Xw4NK5lBl0Pdy/YmkW+TZzHVY6ZMeeuQIyzjlnmWQ5NLbB3sIpOMs3ukB4CD7tIyGx48NM112wa55SpnD80jR2asbQH+5uFjvO1/fp+f+uMfWPUbCYItIiwdwoiGX/IeoBTgOZSqtbYeFoBYTJGKxwKHUJpQl5/HEjbAslD29naWPRb/6y5X65RrdbpT7RMDknEVmrw388R6Wzye/q7kqkNhQ90pKjXNYoiomaqzwZbkPWCVZ5laKtGTTjRE2XgsJkQWxuHJHJcOO4IykE3Rm0lwfMbOtlyt88ypBa7bMcAlG7sZyCZ5LMJk5lpd88ffOgg4YvaVJ6UiTegcIiwdwi/57hxzPnjCPJbWijBDOhkL9Fi81hIbbENhrfkVWPZYgkIlxptprQpTStFtMR15qeGxtITCMnYjYebylRXj+sF+rIsJdw2tCIXZeyxTS2U29izb9maS9HclG02XQdTrmhemclyysadxbNtgtjFiJoxDk0tUapqrxvqIxRRXbupj/2n7rv8njs9xYq7A/3jntYz1Z/j6vtPWtoZPfOcQv/O/fyybN4U2RFg6hF+DI9jlWPwGWDr2wV6H8Vh8q8KsQmHtwx6N2OQDmiSXXNHpTre/ts3Y/cVihURMtYmijcdSr2sWit7Jewgf62IaMJs9FjPM0iYBP7VYajRmGjYPdFk1Ok4sFilUalwy3N04tn0oa106vN/NxVw51gc4BQCHzixZV5WZ0ubX7B7mDXtG+P7zU1YFC4ZvPjPBR762n//96Dh/8A/PWNsJFwciLB3Cb7UwNOVYAqvC6p6hMHA8kWCPJTgUVgjpRSlUqnR5eDtGLPIBHk++5N1cCa6whPWxFKv0ZBIryoXB6dxfKlUDhzouFqtoTZuwDLj3w4TJCE9zVVgmGac7FW+MigliaqldWEZ6naqyMIz4mFJlgG1D9uXKZlCmmW922UgPi6Uqk5ZTAx49OsvukR6GulPcuGOQXLnG82fsPZ6/fPAoY/0Z3vPKHXzlyZNMW7znZsZn8/y3fzzAj4/PRbITzg9EWDpExSLHEiws7dOJDelE8AbK5VCYt8fiPL+/faHcnnx3bN1QWIDXYfIvXuPtbTyWpVK1LXEPyw2TQfZGONqExQ1tzYfMGjMeS2sobUNP2qoqbHKpxMbelaP5h3vTVh/up+dXJv7BKVsuVetW9idmC4z2pRtfRi6LmPzff2qh4e1cv30QgCeOzVnZFis1fnhoire9dIx33LCNSk3znecmrWzBaep831/s5WPfOsgvfuohzkTc+Cmc+4iwdAiTPwmqCgvaIlmqeFeFgRMKC/JYTA7FL8cCBC7sype9x8GYhHyQba7hsXiEwjJ2oTAz/qWZfguvw1dY3Pthsf/pXJmedKLNUxzqTjVmkPlRqdWZy1faPJbh3jRTS6XQZWFmffKmZmEZdLwPmzzL+GyhUSwATcIyGS4s84UKJ+eL7BlzSpy3D2XJpuLWOZonx+ep1DQv37WBqzf3sbEnxXcjCMu39p/hwMQiv3PbFeTLVT77oyPWtuAI23/+yjP83peeshqSKrz4iLB0iODkvW0ozPuvwwmFrb4qDIJ3shR9kvddDWEJ8FjMkrBVeiwLbiisFTMdOaj7fnlO2EqvwdjOhYTCZnNlBrvbRW1jT6qx58WP1uGXhuGeNJWaDg3DTSwUSSViK7ylbW65sk1l2Im5AltdIQInBNebTlh5LM9NOAJiemdiMcXukR7rUJgpa75hxyCxmOL67YP8OMJK5y8/cZKNPWl+5bWX8Jrdw3z5iZORJg78v18/wJ9//wU+/9Ax/uOXn7a2M2itmVoqRXpNIRoiLB3CpkEyrPPeL8fiJO/Dcyx+fSwQ3IviNUQSHEFMxFSotwM+HotFjmWpuHJ7pGEtHks8pujLJBp9Kn7M5CsrKsIMjscSHI4yORgvjwUIzbNMLBQZ7UuvyC0ZoQhrsKzVNSfnCmxpys8opbhkuNuqSdJ4Jlds6msc2z3ay4HTdmG0R47MsHukp1H08LJtA7wwlQsNPYITBvvu85O8ac8IiXiMN181yvhswXq52lKpyl89eJR33LCVX3ntJXzp8RORZqVVanXe+5lHuPH//iYf+JvHI6+hFuwQYekQQVVhNjmWckC5cZjHYhMKCxKmgk8oTClFVyp4773xSFabY1ksVdpKjWF57H5Q970RjlZhAceLCfMaZlvGuRhMjiXoG60RjmGPHAsQmieZWCgx2ptZcSyTjDOYTXJqPlhYziwWqTbNKDNss6wq239qgd5Mgs39y69/xWgvU0ul0NyS1prHj81xw47BxrGXbR0A4MkTc6Gv/eypRRaLVV69eyMAP3HpBgB+eMhuAOcDz05Qqtb5+Zu28e6f2InWzoRoW/7qwaN857lJXn3ZRr765Cn+7rFxa1uAY9N57vr8Y3zoi09a7Rq6WBFh6RAmxxI0lmW1obAwj6UUlLy3CIX59bGAs5MlKBRmHst6CUsmQb5cCyxjXSy2j4OB5eR9UPe9EY7W5Ls5FpZjmcmVV5QaGzZ0p6jWdWAYrnVzpcFeWIorEveGTf1dnA6ZF2YaMJtzLODkSsZnC6Flw4cnc1w20rPCW9o96uRoTJjMj8mlEvOFCle4YTSAl2ztB5zcSxhPn3TOMWJ0ycZuRvvS/PDQVKgtwFeePMWmvgw3bB9ky0AXN+wY5IFnJ6xsa3XNp773AjfvGuIv33cz12zp439997B1SKxUrfHezzzMN56d4G8fOc5v3/NjK7tmvvbUKf7Lfc9yMEIF3vmICEuHqDRyLB4hpYbHEtR5719unA7LsVT9Q2FdKXfvvY/XUa4642D8hCUb4rGYRWBZj9c2guE3a0xr7W6PXF0obKFQIZWIeb7v/q5k6AbK2XzZMxRmtlFO5/zFYcovx7JGYRnrzzTWJfthGjCbcyzgeCzVug71eI5O59i5oXvFsctHHaF4PkRYTA5n98iysPR3Jdm1sZsnx+cCbcGZTdabSTTySUopXnnJBh48PB36AV+u1vne85PcdvUosZgjiq/dPcyTJ+atlsI9fmyWE3MFfvHl21FK8Qs37+DgmSXrddJ3P3ycw1M5PvnLN/A7t+3hG89M8OhR+zE6f/3QMX7184/xye8e5qf/5IeRZ7sdn8nz0fv3c/fDx875EJ4IS4ewGekS2HlfqflWhWUS8cByY78NkM3H/DyWQkB+BiCbDhOWKtlUvPEfvZnGvDCfPEux4oiaVygsm4oTj6nQUNiARxgMwkNhxUqNfLnm47E44hCUwJ9aKtGVjLcVLfSmE6QTscAcy2KxQq5cY7Qv3fbYpv4Mp0PKb1uHXxq2u1OWjwWEw4qVGqcWio3+F8NYf4ZsKs6hyeAPOyMspgrNcOVYr1VV2b6TC1y9uW+Ft3TDziGmlsqho3CeObVAsVLn5ZdsaBx79e6NaG0XSvv+wSmUgtdfPgLAbVePEo8p7nsqfOWA1prP/ugI120f4PVXjPDuV+6gN53gL390NNQWnJDuR+/fz09cuoHv/M7rUQp+/959VrbghOB+6o+/z8e/fYgPfvEp/t2XnrK2Na//4a8+w11//RgPrWLvT1REWDrE8hDK9g/YtVaFpZOxhlfiRaOPxcM+LMeyPDK/3WsAyCaDQ2E5nx4YWJ5w7LeF0sSovarClFKh3fdec8IMA13BobBZj+ZIgzkWVHI85dHDYq57pC+4l2XCnUO2qb/dY9ncn2EmVw4MfZ6YK7CxJ9U2ONQIS1CeZXw2j9a0eSxKKXZt7A7dgHnwzBK96USbKO7Z1MfR6XzgxtFqrc6zpxa4enP/iuPXbRsA4PGQZslH3VloK/M7/fRmEnzv+fBy5x8cnOIlW/rpd0OnG3rSvPKSDVbC8vyZJQ5P5viZ67cCThXkz9ywlfueOm3V8/SZ7x9hvlDhQ2+5kh0buvlXb7iM7z43yb6TdtV0v/f3T1Gta771r1/H+193KXc/cty6xLtYqfGLf/YQn/7BEX50aJpf/NRDfP95u9DjahFh6RBBVWFGbPyEpepOJ/bvvA/2WIrVGsl4+y4XWC4Z9guFGdEwIbNWwjyWfLnqOc4Flj0Wv2GQ5rhXVZg5HlZu7CssWUeU/EIG5sNg0CMUZsJbwaGw9q57w3BPmLA4HslIr3eOBQjMs7T2sBjG+jPEYyqwXPnI1MqO/WYuGe7hhangyrDnJ5a4tCU/A8ujZQ4EhNIOT+UoVetcs6VvxfErNvWSTsRCGzQfPTrD1sGuFSHERDzGzTuHePiF4JBUrlTl8WNzvOqyjSuO33LVKIenchwJEdRvunmcN1050jj2jhu2Uq7V+cYzwXPW6nXN3Y8c43WXDzfyUe+6aTtdyTh/8YMjgbYA+07O873np/i1N17GJcM9/NYtu9k62MVH799vFRL7m4eP8dSJef7kF67nO7/zenZu7OZ3vvBjq7UUq6UjwqKUul0pdUApdVAp9UGPx5VS6mPu408qpa4Ps1VKDSmlvqGUet79Pdj02Ifc8w8opW5rOn6DUuop97GPqdZ//WeRoFCYUopUIubbINlI/PsNoUw4HotfDNqvqgvCk/eFRg+Mj8cSmmNp3x5pCAuF+Y3MN/SH7GSZL1Q9E/fGtq79RW02Z0bmtwuL6W0JGmI5tVj2F5aQ7nsjLF6hsDHXizkVICwnZgtt+RVwPmQ3D2QCQ2FH3cdaPRaAXRu7GZ8tBHpLByeXGiP+mzE9MfsD8hVPn3C+nbd6LMl4jJdu7efx4/7TmbXWPHp0doW3Yrhp1xCHp3KBY3gefmGGal3z6hZhed3lwwChkwO++cwEL9nSz1j/sqBfvbmPLQNdfH1fcPHAQy/McGq+yM/csLVxrD+b5J9fv4Uv//hkaPXiXz14lEwyxs/ftB1winl++5bL2XdygX86cCbQtlip8fFvH+LmXUPcfs0mejNJ/r+ffRmnF4qN6dZngzULi1IqDvwJ8BbgKuBdSqmrWk57C7Db/bkT+LiF7QeBB7TWu4EH3Pu4j78TuBq4HfhT93lwn/fOpte6fa3vz5ZSQIMkQDruP5YlaM4YOB6L1lCpeQtLqeovLGE5lkZzpW/yPhE80qVU8/dYbENhHp334DQ6hiXv+wJyLOA/1mV5Tli7fToRpzeTCM2xBApLwIecCYX5Je8BTi94ex31uma8pYelme1D2WBhmc7Rl0l4CvKlw91ojW9PyXy+wuRiqS2/As7Ms550ojEc04t9JxfIJGNcsrFd1K7dNsC+kwu+Xv34bIGJhRI3egnLziEA9gbso/n+wSlSiVibMO3c2M3ODdlAYZlaKvH48TnefOXoiuNKKW6/ZhPff34qsKz+y0+coDsV55YW+5+/aRvlaj1wrfR8ocLfP36St1+7ZYV3/s9etpnN/Rk+9b0XfG0B7n74GGcWS/zmm3c3jl27bYC3X7uFz/3oiNUU79XQCY/lZuCg1vqw1roM3A3c0XLOHcDntMODwIBSaizE9g7gs+7tzwJvbzp+t9a6pLV+ATgI3Ow+X5/W+kfa+Wr/uSabs06lVicVj7WFCAzpZMw3eV9qCItfg2Twsq9ipe7Zw2JslYKibyjMv8HRHA8cQlmu+udYQkJhSyEeS18meNlXWI4FlrvzW5kNCIWBU3LsJyzVWp2ZfJnhHm/b4R4nT1Lx+fueWCjSm054TisweRe/yrCpXIlytd7Ww2IIm5B8ZDrPjg3dnv9OzQh/v3DYwUnHGzGlyc0opdizqTfQY9l3cp49m/o8Q7bXbhukXHVyMF48dszkV4baHnvJln4yyRgPv+Dv8fzg4BQ37Rz0/AL2usuH+eGhKV9P7Vv7z6D1yjCY4barN1Gu1fmn/d6eQ7FS46tPneK2aza1fXl7yZZ+do/0BPbSfPGxcQqVGr/0ih0rjifjMd77qp386PB0wxP0eu2Pf+cQN+8c4pVNBQ8Av/Gm3VRqmr+P0AMUhU4IyxbgeNP9cfeYzTlBtqNa61MA7m/ztxr0XOMex9tQSt2plNqrlNo7OWk/4yiIss8GSEMqHvP9NmY8Gf9ZYWbvvbe936IucJscA3aymNyLn73jsQSEwso1zz4UWHsozPFYvG2rtTpLpWpgjgXw7b6fzpVRyru5EpzErl/3vdM8CRt7/T0W8E/+TywUGfVI3IPz593flfTNsfj1sBi2DWWZzpV9vcRj0zm2e+RXAHa5I/z9KsOen3ArwoZ7PR/fM9bLs6cXPEO2Wmv2nVxoy68Yrts+ADh7Yrx47Ogs2VR8Rf+MIZWIce22Ad8NmpOLJfafXmzLrxhef8UIxUrd1/6bz0ww1p/h6s3t137DjkE29qS432efzbcPTLJYrPL2a9s/ipRSvOOGrTx6dJbDHjPetNb85YNHuW77ANds6W97/Odv2k53Ks6nv+/ttdyz9zgTCyV+4827275I7NzYzVd//dX8n6+5xNN2rXRCWLy+orf+y/I7x8bW9vWsn0tr/Umt9Y1a6xuHh4dDXs6OUGFJBAiL64n4V4XFV5zXSjEgFAbBy74KoaGwOOVa3ffbtyk39sJ8I/cLE5j8iVe5MTjd9345FiNKfT62DWHx8Xhmc07i3+vbMzi5F79qn0bXfUAoDPyXhZ12x7n4Mdaf8c2x+PWwGIIGWVZrdcZnC+wY8rbtSScY6U1z2EdYDp5ZIpOM+Ybh9mzqY7FY9RxJc3ymwGKx2pZfMYz1ZxjpTfP4MW+v44njc7xs6wBxj7J2cMJh+07Oe/5bM82Xr7rUW1hecckGUokY3z7Q/iWzWKnxveenePOVo55eXjymuPXqTXzr2TOeBTL/8ORJNnSnGhMGWvnp67YQU/DFx9o9hx8emubwZI5fbvFWDP1dSX72xm3c++OTjbydoVR1cis37hj0fe09m/p8IyxrpRPCMg5sa7q/FWjdc+p3TpDthBvewv1tfM2g59rqcfxFoVyte5YaG4KFJTjHYuOxZHzCaODkWQplf1sI8liCJxznSlXPkA447nomGfP99hw0Dgac/zjlat0zROE3J2zZ1uRYvMVhxqc50rCxJ+W77KvRHBnisfgl8M94jHNpxhEW7xxLw2MJCIWB0/fQyql5ZxSMV0WYwZk35h0Ke/7MEpcO9/h+uF855p/ANx331/gIi1KKa7cNeHosxUqNfScXuNb1ary4aecQdY2nMP3g4BR9mYTnt35wvlS9fNeQZ57lR4emKVRqnmEww9teMkahUmtLpOdKVR54doK3vmTM9wvMSF+G114+zN89Nt42MeEvf3SUwWySt75kzPe1/+WrdlHTms+1TIi+Z+84p+aL/OabLz9r4hFEJ4TlEWC3UmqXUiqFk1i/t+Wce4F3u9VhrwDm3fBWkO29wHvc2+8Bvtx0/J1KqbRSahdOkv5h9/kWlVKvcKvB3t1kc9Yp1yw8Ft8ci/8GSFhOwPt7LPXGsEkvulL+I2GMx+KfY3E+9L2+jWmtyZf9k/fgiIZvuXGxSrfbCOlF0FgX48n4Je/7u4JDYbM+41wMQ90pZvNlz3JOv3EuhpEAYanXdWAoDILHupyYyzOQTfqKcVCTpEnKbx9qT54bLhnu8e1lOXhmyTNxbzBDLb0S+PtOzpOIKS7f5G9/3fZBjkzn27ro952cp1rXjX4XL67fMUhMwSMtZcdaa35wcJqfuHSj778zcPIsB88sNZpPDd94doLuVJxX+nzrB7h51xAbe1J8taUf5pvPTlCs1Pmpazf72oJTtnxqvrhirM3R6Rz/+Mxpfu6mbYHRiO0bstx21Sb+6sFjjS9wC8UK/+Obz3PjjkFedZn/dZ9N1iwsWusq8AHg68CzwD1a631Kqfcrpd7vnnYfcBgn0f5nwL8KsnVtPgLcopR6HrjFvY/7+D3AM8D9wF1aa/Op96vAp9zXOQR8ba3vz5Zyte5bEQZOjsVPGGw9Fr+xLqVKzbM50hAUCssHdO3D8hZJr7EspcY4GO8POQiecLxY9B5AaWiMzvcIh4V5LKlEjO5U3DcUNpMr+ybuwem+r9W9x98vTzb2Sfy7x894CMtMvky1rhn18XbAaZKc9mmS9OthMQxkk/SmE54J/CPTjmDs3BjgsWzsZi5faQsD5kpOiMur1NjQk06wfSjLsx4d+E+fWGD3aK9vgQo41UrQnmd53O1vCfJYetIJrt7cz8MteZIj03lOzBVCP2Bff0V72XG9rnng2Qlee/lw4HUn4jFuv8YJhzU3E3/xsROM9TtzzYJ485WjbOxJ8cffOtjIT33824dIxGO871W7Am0B3v/6S1koVviDf3A+Oj/6tf1M50r8/j+7el28FehQH4vW+j6t9eVa60u11h92j31Ca/0J97bWWt/lPv4SrfXeIFv3+LTW+k1a693u75mmxz7snn+F1vprTcf3aq2vcR/7gH4RFy44Hov/P750Ir6GUFhI93zFIsfiE8oqVmoo5f/ajT4YD3sjSt0B3lJPJhEYCvPqujcEzQszjZNmCrIXA9mUv8eSL7MhwGNZnhfWHg6bWiqRTsR8vYZ0Is5ANunpsTQWfAV6LJkV5zbj9LD4C4tSiq1DWY57jEc5NpMnlYgFhuEucRP4reEwk3cJ8lgAtzJspcfiJO7nPZPfzbx0az8x1d6B//jxObYMdHk2lDZz084hHj82t+L/manWeu3lwbnUS4d72DLQtSLP8qPD00wslHhLQCjK8PZrt1Co1LjnEaeuaP/pBb7z3CTvunm757ijZjLJOL/2xt089MIM//jMBE+fmOcLj47zzpu2MeJRkt7KtdsGuOv1l3HP3nFu/e/f4fMPHeN9r9rVaMZcD6TzvkOsKXkfUhVmSon9PJZixb8qDJydLEEeSzYZ9/1mY/InXuLQ2B7p8wELznTkoFCYX0UYLHfke3Xfh3ks5rF5j3JjrTWzuUpgKKwxL8yjMmxqyWmODPo2ONKb9kzeN7ruAz4wTBNeawJfa+16LP4eB8D2oS6fUFiO7UPZwA86U3LcWhlmloBdNuJdEWbYM9bHC1O5FV+CziyWmFoqc02IsHSnE1w+2tvmsTxxbK5RNRbEzbsGKVXrjdEvAA/sn+CykR52eDSENqOU4vVXDPODg8s9KV94dJzeTIJbrxoNtAW4cecQL981xJ9++xCFco3/+cBBsqk4736ld+K9lXfdvJ09m3r5tb95nJ/7Xz9iY0+a33rz5Va2AL91y+X89i2X05tJ8m9uvZwPvfVKa9uzgQhLhyhX66SDQmEJ/wnFy1Vh/ou+wAl5eRHUxwLQlYwFejt+FWHQtEXSw96Ex/y+uYNTSuwXClsoVgNDYYEei8mxBNg7o/PbbXPlGuVa3bM50mA68r0qw5w5Yf6hLPDvvm/MCQsSlgG3SbJFWGbzFQqVWqDHAsu9LK35oaPTed+KMMPWwS6ScdVWGXZgYpFUPBaY+Ae4clMvdb1y/L4RCptv0NdtH+DHx+ca1/7CVI4TcwVu3tXev9LKa3YPk0nG+MqTTs3OQrHCQ4dnAhPvzbzjhq3ky47XcWaxyNeePsXbXro5MBrQzL++9Qoml0q88b9+m68+dYpfee2lbdtN/UglYnzufTfz09du4darRrn7zlcEfvFpJR5T/PqbdvN3v/oTfOCNuwPzSS8GIiwdolyrk0yEVIWFNkiuzmOxCoX5iVI5WFjMuBavXpbGyPygUFg64Ts2f6lYoTdAlMJyLImYCnztgWzSM8cS1hwJy/mTKQ9hmVws+TZHGoZ7vLvvjVgMBwiTEZ2TLZVhjanGIcKybShLqVpf8fpaa47N5H17WAyJeIwdG9orw545ucDlm3pIBnx5AsdjgZWVYY8enSWViPlWZTVz7bYB5gsVXnDzQSaU9YYrwsWhO53gzVeOct9Tp6jU6nztqVNU65pbr9oUamte+5WXbOCPvvkcd37uUao1zZ2vte/zuHnXEP/9565lpC/Dr77+Uu56w6XWtuDMjvvoO17KH73zOnZ6TCc4nxBh6RBhyfugkS4NYfHrng+YUFyva8rVerCwpPxzLPmA5kpoLjduFwdzzK/c2DwW1CAZHAoLqApzu+6DwlH9Xd45FuOFeM0JM5hvi17zwkwoLIiRvgxnFtr3qp9ZLLKxJxX4Ad2dTtCXSbR5LMs9LOHCAiunHE8tlcmXa6EeCzgzw5o9Fq01z5xc4MpNwaEscLylrmScZ5sqwx45MsNLt/QHJsAN17mJbpOw//Zzk1w63N14T2G8/dotzOYr3LP3OJ/87mGuGO3leoswGjjhsI/+zEvp60qy7+Q8/9cd17Ar4gf826/bwpfvehX/9vY9viXGFwMX7zvvMGE5lqCRLuWQkS6ZgKowcyxIWDIhDZJdAVVdQX0sJsfiN4QSnOT9anMsqUSMrmTcMxQ2HzAnzGC2SLZ+uJs5YUGhhmQ8Rn9Xsm3Cca2umcn5zwkzDPekKVXrbe/99Lz3gq9WNg90teVYTNPj1tAcS3vJsVkqtcPig/KykR6OTOcaIdrJxRLTuTJXheRIwAnJ7BnrbWyTLFZqPH1inht2BldGNV57uIeR3jT3P+2Mo3/w0LSVt2J4454Rrts+wO996WkOTeb44Fv2RKqM2r4hy3d+5w38+Pdv5Rdevt3aTliJCEuHCKsKCxzpYtt57+HxLE8nDi43DtrHEmRrSom9hcWtCgvoY+lNJyhX623vvVqrU6jUfAdQGvq6vEfnLxSrocIymE1SrWtyLdduQmFBDZLgPS9sNl+mrv1LjQ1+TZIn54psDigXNmzyaJI8Mu30sPT7THQ2bBnoQqmVwnLA9SD2eIxEaeXabQNUapqnTzg2+9wqr6vGwoUFnD32TxyfY6FY4bGjs1Rqmps8Znx5EYs5Y06+tX+CX/nLvZRrzn57W2IxxaffcxO//qbd/Nm7b+QNe+xFyRCPqcASeiEcEZYOEdrHYlMV5jcZudF53/7hbo6F5VgqNe05lqUQVlGWdIZYFgJCYWF9LNBeVWYqb4I8FsB32dd8oeK7x8Uw4Hbfty78auxiCUmObuhJtVWFNXpYQpL3I+7IltZw1sn54D4Uw1h/hlMtgyiPTLWvFPYik4wz2rtyfP7+04v0ZRKBRQOG691wlFm7+7TrfeyxFJbXXzFCze0B+drTp8kkY/xEhEa9X3ntpYz2ZXjkyCy/+PLt7B4NF8NmBrtT/PYtl3OLRTWXcHYQWe4Qa+u8d0TJrww0GY8RjynPUJiVsKSWczStsf1CxX8DJDhx52wy3vatH2DJ9ViCqsKa54U1f5CHDaA09GW8d7IsFipsC8k19DcNotzaFImZyZWJx1SoMA11p9r2kk+GdN0bjHg0z81aKFZYLFbZPBD+4b510BkmuVSqNv58j07nuckypLRzY3ZFyfD+04vsGbObDTXcm2bHhmyjbPehF2bYs6k3sLS7mRu2D7JtqIv/ct9+5gsV3nLNpkgeQH82yf2/8VoOTS1x7dYBazvh3EE8lg5RDlgtDE7+pFbXVD3EpVStBdo69t4lw2E765sf88qzBC0JM2TTCc9QWL5cRSkCS52NcLQOB7QVFr9lX1Y5Fp9y5dm803Uf9iHrTDhe6e0sd90HC8tYvxOOOtHUqGg8kOZlUX5cOuz0k5ipt8VKjZPzBetqoSvH+jhweoFaXaO15sDpRaswmOGG7YM8enSWpVKVvUdneMUl9h5HLKb43dv2MLlYIhWP8Wtv3B1u1EJ/Nsn12wdDmwuFcxPxWDqEzRBKcDyb1mqRUrXuWxFmyCTjPh6LSd4H51gAih6DKB2PJURYUnHPqrBcqUZ3KhH4AW1yKO3CEjzZ2NDXleS5MytHhGitA3exGEwPQWtl2EyuHNjDYtjgzgur1XWjL2Bq0REav8nGhlQixkhvmpNNHou5bZNjuWzEEZCDZ5Z46dYBjs04u+ptq5SuGuujWKnzwtQS6UScpVKVPRZVXYbXXTHMFx8/wX/88tMUK3Vuv8auZNfwz162mctHexnIJq2KFYQLCxGWDhEaCnPFpFyt05ozdryd4A/3dMJ71liUUJiXx5IvVwP7WMDdyeJTFRaUuIflxH5rybF9KKw9eV+o1KjWdWBzJDSPzm/1OsqNzvogNnSnqGsnR7PBFZJT80W6kvHAUTKGzQNdK0Jh5rZNjmXHhm4SMcUh12MxO9nDOsgNZu7W3iOzjb/fl1j0kRhuu3oTI71pvvjYCfZs6uXmnXbJ92a8dqcIFwciLB2gVtfU6ppUPKAqLLEsLK2UQsJo4AiH19j8xmrhkOQ9tAtLva4pVuqBthDgsZT9990bjHC0lt2Gjcw3mFBYva4bYRGbcS7Nj7d6LFNLJV5qEbsfcsVkJrcsLKcXCowNZKxyFVsGuniqabvfqfkCiZgKbI40JOMxtm/IcvCMIywm17PLUlguG+lhY0+aHx6aJp2I0ZdJWJULGzLJOH/xL27mi4+N80uv2CEhKSESIiwdwFRbhSXvwacXpVILtIUgj8WujwXaB0kWq8FLvgzZVNxzgVK+XCMb4rGYUFhrVViUUJjWsFSuNjVMOs8VJiyZZJxMMtaWY5leKoeWCwNsdIsNppbK7HYLjE7NFxt76cPYMtjFP+6baIjiybkim/oz1uM2LhvuaSTgnz65wOb+TGipsUEpxZuvHOFudyjiT1+3JfKYj6s293HV5qsi2QgCSPK+IxixCGyQDGlytEve+/exBOZYmqrCVtiGLPkyZFNxz5EuSyX/ffcGv1DYgm0orKu9+94IhU04aqArtaLcuFipsVSqhibfAYZ62ueFnZ4vsqkvPJQFjsdSrtUbCf+j07nQrvlmdo/2cGQqR6HsNBlGnVb73lftbNz+lxbj1wWhU4iwdIByBGHxDoXVwnMsyXhgjmU1obCwtcSG7lSCfMW7jyUslGVCZV6hsGRchQqq8VKavY4Fy1AYtA+iNOXCYcl3aJpw7HbfV2t1ziyW7D0WN5diRtgfnspxyXDw2PlmbtwxRLWuuX/fKV6YynHtNrtSY8OeTX3c/5uv4Wu/8Zp1HaEuXHxIKKwDmP6UlGVVWCulaj30AzqdiHmGo4yw+G2fhGVhaU3A23osXT4eS75UI7sh2DYWU84gSo9QWG8meNYXLItHcwK/4bGEhNHAGTTZ3D1vvIcNFqGwwWySmFoWo8mlErW6bkwfDsOUDB86s8Qud4HWJRFmT920a4hkXPFbf/tjAN6wJ3iniBdRKsEEoVOIx9IBbDwWk9j3Gn0f1gMD4cn7oFBYJuU85uexhJUbd/v0sSyVwpP3jn3csyosLAwGy+Guec9QWLiwjPalVyzMauyrt/BYEvEYY/1djV4UM7vL1mPZPpQlk4xxYGKRA6fNPhN7j6UnneCnXrYFgJdtG+CKiB3ogrBeiMfSARrCElAVZvpU/DyW1Zcb14kp/3Ew0NzHstI+b+uxuEMsmyuzwJQbh/8T6kknPBskrYTFJOybmiRn82Viyi4UNto0ZVgpZT2SxbBloItxV1jMeBbbHEssprh8tJdnTy00KsGilPwC/MEdV/PSrf28cc/Iuq2ZFYSoiMfSAayqwuLBOZbwqrC45xDKoruLJehDx6/z3jrHkm63r7nDHW3EoSeTbBOWuXy5McsrCFMF1Zy8n1oqM9SdsqpyGu3LUK7VmXXzLFNuWCtoLXEzWweXe1FMg6OtxwJww45BHjs2y4OHp9k+lG2ULdvSk07wnp/YaT02XhDOBURYOoBNVVhgH0vFJhTm7bGELfkCpyciGVdtwmI8mDBhMWP1mxd2mdtWwpJuL1e26ZwH6EklUGqlsMzkSlYNjkCj69uEw6ZzZXozCeutgFsHuzg1X6BUrfHCVI7+rmSj8dKGV1+2kWKlzrcPTPL6K6LnSAThfESEpQMsh8IshMU3FLZajyW8wRHcnSyrDIV1p9r7YEzOJKzowJzTmmOxmfUFTjjJGUS5bD+9VLZKvoOTY4FlYZlcKllVhBkuG3VW7R6ezHHwzBKXDndHCkm97vJhrhzroysZ55deYbf/XBDOdyTH0gHKFqGwRh+LhziUqrXAqi5wPJaiV46lWgudMwbeO1lsQ2EmuZ9rqgxrdM5beSwrQ2Fm1pftN/++rsSK5P10rszVll3krR7LxHyxMdLehstHnWT7cxOLHJpc4o0R93sk4jHu+ZVXUK9j3dwoCOc74rF0gCgeS6nFY9FaW1WFpRPOTpVafeU2xGLIamFDV6p9i6R9g6QjHoWmXhbbznnnnJXJ+3y5RqWmrcew93clW3Is4RscDSMNj8XJrYzPFtgSsoGxmV0bu0nGFV976jRTS2Wrve2t9GbCl3MJwoWECEsHsGqQdCvG2jYp1jV17b890mDKiVvzLMVqeI4F3Mqu1j4Wi+ZK8PZYFiOEwrrdHItZEWy8jwFLYenLLC/7KlVrLBar1sn3dCLOUHeKiYUi5WqdicUiWyJ0v6cTcW7cMcT9+04DRBofLwgXKyIsHSDKrLBWYbFJ/IN/KK1YqQf2sBi89t4XKjVS8VjbGP9WvNYT226ABCcUVnMHXsLyUEhbj6V52ddszvkdpbpqpNfpZTk9X0Rr2GoxXbiZt750DHD6UnZH6EMRhIsVybF0AKsGyYS3x2EaJm1Gujj2K4WlUK4xaBFm8cyxlGuh+RVY9liaJxxHSt43LfvqSsWXpxNbhoecUJjzelE65w1bB7Mcmc5xZNoZ6Bi1dPeXXr6dbDLOTTuHpJdEECwQj6UDlGrhOZZ4TJGIKV+PxTYU1ioORYvEP/jnWGzyM2aCsZfHYpe8j6+wmXf3o1h7LE3JezOexTYUBnDFJmeYoxlhH3VPiFKKn7lhK9s3SC+JINggwtIBbDwW87ivsISEs4xH0+qxFMs1MiHeDnjnWPIVW4/FTd432Zvy3x6LkS6NLZJFIyxujqV145kPQ91pCpUauVKV6YbHEqWyq9cZ5vj0aYZ70wxFECVBEKIjwtIBypZeRyoRa+tjMaGxoHEwEOSx2OdYWmeNFcpVO48ludLjAEcketIJqwVQJg9j8iRRcyym0/3UfHFVobDr3KnAT52Y5zp3s6IgCGcPEZYOYIQlGZIET8XbPRabnfXg77Hky9XQIZIAXalYWyhssVi1CmWZCcWLTU2KS6WKVX4FaHgIZq/JXKFCIqYajZdhLAtLgROzBXrTCXotXxtg+4blpPvbXrbZ2k4QhNUhyfsOUK7ViMdU6OyqdDLWHsqy2FnvPN7usTRWC1uEo7xCYblyldFeu7lXvZlEo3cFHO/FRpRgWVhm3YVbZpyLbSJ8s1vFdWquyPHZAluHspGT6J9+700cOL0YucFREIToiLB0gEpNBybuDV4eixGa1XgsphPfymNxy43NlF9wwlmXbLT7J+AIS3ODpN10YljuV5l2R9bP5yuRGgZH+zLEFIzP5jk2k4+008SwbSgrgxwF4UVCQmEdoFythybuAVKJuK/HYjM2H1aWK5sqLRthyaTahWmpVLP2Opp7ScANo1mGoxLxGAPZZCMUNp0rMWSZuAcnN7VzQzfPnFrk+Eye7SIQgnBOI8LSAUrWwtKevLcPhZm99cv2tiNZms9ZMUgyQp6k1WNZKtl7LOCEw2bcUNjkYinSvC5wSoS/+ewEpWp9VWNVBEF48ViTsCilhpRS31BKPe/+9lzKrZS6XSl1QCl1UCn1QRt7pdSH3PMPKKVuazp+g1LqKfexjyk3rqOUeq9SalIp9YT783+s5b1FoVytW4XC0olY2wbJknXy3t9jsSkZbt17X63VKVbCVyIbels8lqUIHgs4fSemVPjMYokRy9yOoVlMrpXKLkE4p1mrx/JB4AGt9W7gAff+CpRSceBPgLcAVwHvUkpdFWTvPv5O4GrgduBP3ecB+DhwJ7Db/bm96eX+Vmt9rfvzqTW+N2vKNTuPJZOMU2wNhVXtPJa0h8diOuHtqsJWCouZ+2WzARKcJsWVOZaK1QBKw0hfhomFEsWKM+tr2HKDo+GfX++s6L1kYzc7pFFREM5p1iosdwCfdW9/Fni7xzk3Awe11oe11mXgbtcuyP4O4G6tdUlr/QJwELhZKTUG9Gmtf6SdiYaf83nNF5VytWblsWQ8PJblHEt0j2U5FBYuDpmWUNiSWdQVwWNZLFYa05hz5Zr1EEmAzf0ZTs4VOONOGY4qLGP9XTzwr1/HV3791TJWRRDOcdYqLKNa61MA7m+vWs4twPGm++PusSB7P5st7m2v5wL4GaXUk0qpLyiltvldtFLqTqXUXqXU3snJybD3GEqlpu09ljZhqTceCyKdiKHUyr31UZL3raEw0wVv67EMdCWp1DT5co05N1cyEKGDfay/i1K1zjOnFgDY1BctFAZw6XBPYwqAIAjnLqGfhkqpbyqlnvb4uSPM1jyFxzHtcczGJui5/gHYqbV+KfBNlj2hdgOtP6m1vlFrfePw8NrXxdpWhWWSsbbu91LV6YEJa65USpFNxlfM68pX7IXF7K3Pud3zUWZ9AQw2NTma/fE2wy8Npsnxh4emAGfPiSAIFyahnypa6zf7PaaUmlBKjWmtT7lhqjMep40Dzd7DVuCke9vP3s9m3L3d9lxa6+mm438GfDTsvXUK2+S9k2Np91gyFqIEkE0nyDUJi+3OelheyLXUKixpu+73wexyk6MRt8EIJcNmgOO39p8hFY81mh4FQbjwWGso7F7gPe7t9wBf9jjnEWC3UmqXUiqFk5S/N8T+XuCdSqm0UmoXTpL+YTdctqiUeoVbDfZuY+MKk+GngGfX+N6sKUVI3rd2vxcrdou6wNk93zy6fjl5b7d3HpZDYLmGsNh5HUPdznkzufJyKCyCx7J7pJdUPMb4bIFtQ12hUwoEQTh/WWvA+iPAPUqp9wHHgJ8FUEptBj6ltX6r1rqqlPoA8HUgDnxaa70vyF5rvU8pdQ/wDFAF7tJam0/kXwX+AugCvub+APy6Uuqn3PNngPeu8b1ZYx0KSzgjXZq7351FXXbCkk0lVmxxjBIKMyEvU9m1nGOJ5rHM5SuNPE0UjyWViLF9Q5aDZ5Z4uWxhFIQLmjUJixt+epPH8ZPAW5vu3wfcZ2vvPvZh4MMex/cC13gc/xDwoQiX3zFsq8Kal3U1Gh6rtdCKMEN3eqXHUijXUCq8ogyWx9svtoTCei09FiMiM7lyQ1iijp//N7dewb//+6d4502+dRWCIFwASIlNB4hSFQYrw1+lit2iLnA8lrnCcpNi3l3UZVN+ayYUG0/FCIutx9LflSQeU0znSiwWq/R3Ja09LcPt12zitqtHpVxYEC5wZKRLB7BN3nd5NDna7qwH12MpNedYalZhMIMz+t4RplypSiYZvu/eEIspRnvTnJp3dsevplwYEFERhIsA8Vg6gH3nffvo+1LVbgMkOB5Lc7lxoVy1qggz9GQSDU9lsRRtJAvA2EAXp+aK5MtVRvtXJyyCIFz4iMfSAUqVmvUWR2BFyXEkjyUVJ1du8Vgsuu4NvU3CkluNsPRnODlf4PRCkdGInfOCIFw8iLB0gGK1Hjr2Hpo9luZQmH25cTadIN9UFVaw3Flv6MskG2uBF4tV6657w5aBLo5O55lYKMluE0EQfBFhWSPVWp1aXVtVZpmQV3MorFiN1sdSrtUby8IKEXMsg9lkY4vjbL4cuapr92hv4/Y1W/oi2QqCcPEgwrJGilW7WV/QPKF4ZSjMttzYNEKaJsuoyfuBbKrhsczmypH6UABevmuocfvqzbITRRAEbyR5v0bMtOK0VY6lPXkfqfPezPsqV+nPJilEsAWn72SpVKVcrTOTi+6xbB3s4hdevp0dQ1lGV1kVJgjChY8Iyxoxq36tQmEe5calat1KlGDZYzFNkvlyNXIoDJzVwAvFamSPRSnFf/npl0SyEQTh4kNCYWvEdrVw8znGpl53dpvYlhsvTyhuDoXZfzcYcIXkhckcsDz/SxAEoZOIsKyRSB5LYmUorBQhPwPLHkuuXKVe1yxFLBk2oa9Dk0vA8ih8QRCETiLCskaWN0Darwc2Cf9lb8e2j8UNhZVq5MpVtHZWBtsy2uf0njx+fA6A4R7pRREEofOIsKyRhsdik7xvKTc2jZI2ogSQbUremynFUfbObxlwek8eOjwDIL0ogiCcFURY1shyKCxcHGIxRSq+vEVyeS1xRI+lXGsSFnuPpSsVZ0N3ihNzBRIxJZVdgiCcFURY1kjUcFY6GVv2WCIk/qHJYylVG8Mko3gsAFsGnc2Nmwdk2ZYgCGcHEZY1EsVjAUdEStXlqi6wW9QFkE0uV4WtxmMBuGrM6Zi/ZFh2zguCcHYQYVkjy8l7uz/KTDLW6JwvNITFThwS8RjZVJyFYoUF12PpiygsP3vjVgB++RU7ItkJgiDYIg2SayRqyXAmEW/kVnKNnfVRmhxTzObLq0reA9ywY4gn/9Ot9EW0EwRBsEU8ljUSZaQLOAJUbITCzBZHe30f7HYmFM8XjMcSXSBEVARBOJuIsKyRKA2S4ITCTPjM5Fi6I3osM7kyU0slulPxSGPzBUEQXgxEWNZIqVJDKaxWEwN0pRLL04nd0SxRxMGZUFxmeqnMRlm2JQjCOYgIyxpxlnzFrHe596abtjg2ciwRxrJkk8zmK0znSmyQkSyCIJyDiLCskVLE0fXd6XhjiGSh7Kw0jtJPMpBNMV+ocHq+yAYZySIIwjmICMsaKVXtF3WBk6jPNXks3RG8FXDWAwMcmsyxUYRFEIRzEBGWNVKs1KybIwF60gl3gKQmX4q2sx5gx4bl+V6b+2UkiyAI5x4iLGukVK1bj3MBx2OpayhUapFXCwPs2LDcMX/lmOydFwTh3EOEZY1E9VhMz8pSqcpiqRK5p2SkqRLsys0iLIIgnHtI5/0aiZpj6XEHSS4Vq8wXKoz0RgtnxWKKr/zaq3ni+JyEwgRBOCcRYVkjpWqdrihVYWYLZKnGQqHKZcPR/wqu2dLPNVv6I9sJgiC8GEgobI04obAoHstyKGyhWKGvS8arCIJwYSHCskZK1br1nDCgISTzhQoLheg5FkEQhHMdEZY1UqzUGiuHbRhyu+XHZ/PUI+6sFwRBOB8QYVkjUT2WwawjLEemc4BMGhYE4cJDhGWNRC037krF6UrGOTqdB5AciyAIFxxrEhal1JBS6htKqefd34M+592ulDqglDqolPqgjb1S6kPu+QeUUrc1Hf+wUuq4Umqp5TXSSqm/dW0eUkrtXMt7s0FrTWEVTY5D3SkOnF4EkLEsgiBccKzVY/kg8IDWejfwgHt/BUqpOPAnwFuAq4B3KaWuCrJ3H38ncDVwO/Cn7vMA/ANws8e1vA+Y1VpfBvx34KNrfG+hlGt1qnUdaVEXwEA2yZnFEgBj0osiCMIFxlqF5Q7gs+7tzwJv9zjnZuCg1vqw1roM3O3aBdnfAdyttS5prV8ADrrPg9b6Qa31qZBr+QLwJmU7y36VmH0qURZ1AY2pxErBaJ8IiyAIFxZrFZZR8yHv/h7xOGcLcLzp/rh7LMg+yMaPho3WugrMAxu8TlRK3amU2quU2js5ORnytP409qlE9FguG+4BYCibIhWhB0YQBOF8IPQTUSn1TWCTx0O/Z/kaXl6DXk8brfUngU8C3HjjjWHP68vyauFowrJ71BGWs+tPCYIgrA+hn4ha6zf7PaaUmlBKjWmtTymlxoAzHqeNA9ua7m8FTrq3/eyDbPwwNuNKqQTQD8yE2KwJs1clm44WCrtp5xAA//4nrwo5UxAE4fxjrXGYe4H3uLffA3zZ45xHgN1KqV1KqRROUv7eEPt7gXe6lV67gN3AwxGu5R3At7TWq/ZGbFitx3LZSA/7//PtvP26sOieIAjC+cdaheUjwC1KqeeBW9z7KKU2K6Xug0a+4wPA14FngXu01vuC7N3H7wGeAe4H7tJa19zn/kOl1DiQVUqNK6X+k/tcfw5sUEodBH4bjwq1TtPwWCIm74FI64wFQRDOJ9Y0T0RrPQ28yeP4SeCtTffvA+6ztXcf+zDwYY/jvwv8rsfxIvCzES5/zTQ8lojJe0EQhAsZKUlaA6YqLGq5sSAIwoWMCMsaWCqurtxYEAThQkaEZQ3M5isk40o8FkEQhCZEWNbAXL7MQDbFWW7wFwRBOK8QYVkDs/kyg1mZTiwIgtCMCMsamM1XGHD3qwiCIAgOIixrYC5fZkD2qQiCIKxAhGUNzOYrjY2QgiAIgoMIyyopVmrM5MqM9smiLkEQhGZEWFbJcxOL1OqaK8f61vtSBEEQzilEWFbJvpMLAFy9uX+dr0QQBOHcQoRllWzoTnHLVaNsHexa70sRBEE4p5BZJKvk1qs3cevVXvvPBEEQLm7EYxEEQRA6igiLIAiC0FFEWARBEISOIsIiCIIgdBQRFkEQBKGjiLAIgiAIHUWERRAEQegoIiyCIAhCR1Fa6/W+hnVFKTUJHF2l+UZgqoOXs57Iezk3kfdy7nGhvA9Y23vZobUe9nrgoheWtaCU2qu1vnG9r6MTyHs5N5H3cu5xobwPOHvvRUJhgiAIQkcRYREEQRA6igjL2vjkel9AB5H3cm4i7+Xc40J5H3CW3ovkWARBEISOIh6LIAiC0FFEWARBEISOIsKySpRStyulDiilDiqlPrje17NalFKfVkqdUUo9vd7XshaUUtuUUv+klHpWKbVPKfUb631Nq0UplVFKPayU+rH7Xv5gva9prSil4kqpx5VSX1nva1kLSqkjSqmnlFJPKKX2rvf1rAWl1IBS6gtKqf3u/5tXduy5JccSHaVUHHgOuAUYBx4B3qW1fmZdL2wVKKVeCywBn9NaX7Pe17NalFJjwJjW+jGlVC/wKPD28/TvRAHdWuslpVQS+D7wG1rrB9f50laNUuq3gRuBPq3129b7elaLUuoIcKPW+rxvkFRKfRb4ntb6U0qpFJDVWs914rnFY1kdNwMHtdaHtdZl4G7gjnW+plWhtf4uMLPe17FWtNantNaPubcXgWeBLet7VatDOyy5d5Puz3n7DVAptRX4SeBT630tgoNSqg94LfDnAFrrcqdEBURYVssW4HjT/XHO0w+xCxGl1E7gOuChdb6UVeOGjp4AzgDf0Fqft+8F+CPgd4H6Ol9HJ9DAPyqlHlVK3bneF7MGLgEmgc+4IcpPKaW6O/XkIiyrQ3kcO2+/UV5IKKV6gL8DflNrvbDe17NatNY1rfW1wFbgZqXUeRmmVEq9DTijtX50va+lQ7xKa3098BbgLjeUfD6SAK4HPq61vg7IAR3LFYuwrI5xYFvT/a3AyXW6FsHFzUf8HfB5rfUX1/t6OoEbnvg2cPv6XsmqeRXwU25u4m7gjUqpv1rfS1o9WuuT7u8zwJdwwuLnI+PAeJMn/AUcoekIIiyr4xFgt1Jql5v0eidw7zpf00WNm/D+c+BZrfV/W+/rWQtKqWGl1IB7uwt4M7B/XS9qlWitP6S13qq13onz/+RbWutfWufLWhVKqW63MAQ3bHQrcF5WU2qtTwPHlVJXuIfeBHSs0CXRqSe6mNBaV5VSHwC+DsSBT2ut963zZa0KpdTfAK8HNiqlxoHf11r/+fpe1ap4FfDLwFNubgLg32mt71u/S1o1Y8Bn3erDGHCP1vq8LtO9QBgFvuR8hyEB/LXW+v71vaQ18WvA590vx4eBf9GpJ5ZyY0EQBKGjSChMEARB6CgiLIIgCEJHEWERBEEQOooIiyAIgtBRRFgEQRCEjiLCIgiCIHQUERZBEASho/z/s4XXSjRXHSoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,si(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f12ee00",
   "metadata": {},
   "source": [
    "### 2.前向差分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e629f564",
   "metadata": {},
   "outputs": [],
   "source": [
    "def qian(x):\n",
    "    h = 1e-5\n",
    "    return (f(x + h) - f(x)) / h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e2debca2",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x171e50f0a00>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tIoaQqn2tnETJaa5Ugar44PfVbBhtXpKcbibzJazvitbOepjOWqlyJPMltOrVTF2xoKdUkmiO+/Xtq3BkJIXTNFKDIJY01PkMQPX7UZKMGBqFQQzUc+tetvIYRLObjMeQK5abuq69PNyTufpUUiykSFc0zeRK4BzGkqDWiOq5ogkA+trC6G+LGB3UXphIF3BiLO3+iQRBzBkSBmgRQ0EiYiiWq1D9s4sY8hYRg5fO51yp0iQM0aBcKolzXmc+A5qopGTHaWRr4zQAoMXjkqChaa2CaWVrGP1t4VmVuv7Ot3bijv/xAl49OeH5LEEQ3iBhQM18dhtmVyhXmjwGsTPaNZUkIgZTuavfxxBUfJLmc7Vu1zSgGdAyEUOhXEW5yo0SV0DzGGTHaYjoQEQMLeEAUvmya++GwIgYdGEYnsmhJCHEgtPjGezVfYl/e4MG+BHEQkPCgFp6p1RxftAVy9WmclVZ81mkmhrPhyVHb+eKzc11ccl0kPj6sWB9xCCbSpq2iBgALT0lw9CMJgw9iRC6EyFUudbsJsues1MAgHWdUbx+alL6HEEQs4OEATDSQ04GdFkfadEUMShyDW7GvuiGBrmw5GrQfKmCcMPZiKpI+RMi3RQxRRyxYAC5UgVliVfuUxYRAwDpdNJ4uoD2qApV8aEzphrXZDkykoLq9+GurStweiIjPc2WIIjZQcIArVwVgGPJqhCNZmGQNJ9tIgZtNajcLojGVJK26Ec+YjCnkkSDnMw+BxExiKokIRCywjCRLqIjqp1tj2qd014ihiPnU9jQHcOW3gSqHLOa7vrqyQnMeDDMCWI5Q8IAbVYS4CwMwiNoNJ9lq5LsIgZpj6HYbD6HVT+yEg92MYHVHDHEdZFISfQyTGdL8PuYsSRIRAyy01nH0wV06JGC+NuLMAxO5bC6PYwNXTEAwKlxb8Lw2K4B3PfQq/j9f97j6RxBLFdIGFCLAmQihmDTg91dVABnj0FmbLfVAL+I6kdWYgOcEA+riEHGvJ7KFtEaDhib67ymkibSRXTEtEhBRA7jaXlhOD+Tx4pECH1tYQA1M1uWf90zCAB46dg4RmZo1zVBuEHCAJMwOOTbxYO/KWIwUknuHkPAz+oa1AD5DXBW5aoRVUGlyl2b86wiBi/TWaezJWOHAwDjbS8eQ6cuCIlQAH4fw2RGzmPIFMpIFcroaQmhJRxAPKjgnAdhyJcq2Hl6Crds7AQA7DxN5jVBuEHCAJP57JRKKrt4DBJVSY3RAqBFDFINbjYeA+A+a0n4EFG1OWKQ6WWY0uckCbxUJZUqVSTzZcNb8PkY2qMqJiQjhpGk9gp/RSIEQOuF8CIMx0fTqFQ5/t0NqxAK+PDmwLT0WUFZYqw6QVxKkDCg9nB3euVdG5td/3BmjEH1+6Q8hsauaUDzHGRWg1p5DEIYMi7CIAxmK49BJmJI5cuGvwBov4NQwCe16Ef0SrSEa+c7oiomJD2G8w3C0Nsa8pRKOjKSAgBs6U1gQ1fMc/d0pcrx0f/zGt75Vz837oUgLnVIGCDpMRgeQfOvLKj4JPYxNK8FBbRUktsr/mqVW54XG+DcZi2JiCEyS48hUyjX+ROAfPeziCrMA/w6YiomJMtVxcO4p0UThq5YUDraAIDjY2kE/AxrOyJYPwtheP7IKF4/PYnBqZwxOpwgLnVIGAAEJFJJRZtUEqAZ0jLlqpYRg4T5LMZpNKWSJEdqiIjBHHF48RjShXJdcxwAtIZVOWHI68JgmtPUHg1KVyWNzGgCIiKGzngQE5mCq+EuGJjMYmVrGIrfh/WdUQxO5Tz1Qbx4dAyhgA/X9LfgpwdHpM8RxMUMCQPM5rP9A8OujwHQUituHkO+VDHGZ5jRzGfnsyKiiDQKQ1BOGIRxbTa+hd+Qyrs/3K2EQT5i0ISnLmLw4DGcT+YRDypGxNIRVVGqcOPrujE4lcOqtggAoL8tDM7hKSW08/QUbljbjps3duLwcMpzc12pUsVzh897mi1FEIsNCQMkzWeL6agCmQ1wdhFDWPW5ms85oweiuSoJgGuTm5YKqj/r8zGpQXrVKke2WGlKJSXCAakJq0J4zAP8OqIqUoWyVJnuyEzeSCMB2i4IANJjvwencujXy1x7W8LG15ShVKni+GgaW3oTuLq/FeUqx8HhpNRZwZ88cQC/861d+OPH93o6RxCLCQkDzBGDfXrCKWJQFR8KbtNV7cxnxY9KlTsOlTPWetqYz24RQ7ZYMUTETDTo3iAnSl0bI4ZESG6An5FKMkUMrXrpqkwn8mgqj25dDACgQ69ukhmpUShXMJ4uYGWrJggrWrSzI5IRw+nxDIqVKjaviOOK3jgA4Ph5eY8ilS/hX3bVVpoOz3ifKksQiwEJA0xVSTIeg9/KY/BLeQyW5rPEdFaxva2p81naYyg3paEAreEt7RptNDfHAfLTWY1UkiliMMpdJdJY09kS2qK1UtnOuPa2TCpK+BidenPdCj1iGJaMGE7qHdYbu2Pob4sg4Gc4MS4vDK+dnESpwvGnH9wCAHjhyJj0WcFoKo/RFFVDERcWEgZ4q0qy9Bj8ElVJdhGD6EVwEoaStfksHtbufQzNqSBA8xmyLq/6xfrPWKhRGAJIF8quJnAyX4KP1fdQCJGQybtP50poNUUb4iEvEzEI8RBjOGJBBfGgIp1KEguF+tsi8PsY1nREccrDnKadZyah+n24b8dqdERV7DozJX0W0How3vXXL+C9X34RA5NZT2cJYi6QMMDsMdg/YO36GAD5qiTrclX3Bjl7j0H0Mbi86i9aRwwR1e/aAyFWh8YaPIpYSOu6dotWkrkS4qEAfCbju9Yg5+5vTGeLxtA+QBv97WOQKnedMCKGWsSxoiUkndI5N5VDOOA3dl2v7YjizIT8A/r4+TTWdUYRCvixta8F+89523X9jV+cRLpQxlS2hG+/ctrTWYKYCyQMAAJSDW5OVUk+985n2wY3iYihaO0xBBUfGJOIGAoVS2GIBRXXDXDi41G1OZUEuPdBNG6OA2p+g1sqKV0so8q10liBX++cHpNIJQnxEF3XgCYMshHDueks+trCxoyovtaQsVtChuNjaWzs1gb/be1L4PhoWspwB7Stez87eB4fumYl7ryiBz/e771U9tR4Bg+/dJKmyhKeIWGAXFWSMUTPplzVrSopbxMxhCU8hrxNKokxhkjAfdFPplhuerADWsOb21nx4G/2GLSHu1u5azJfv2saqPU0uKWSZhr2QAg6osFZpZIAoLclJO0xnJvOoU83rgFtHEcqX5Yq8c2XKhiYzGKDLgwbu2MoVzkGJuWE5ej5NMbTRdyyqRO3burE4FTOUzqpUK7gtx5+DX/x5CH8waNvSJ8jCICEAYDcPga7sduAZOezS8Tg1MuQs6lKAuQe7tlixeh5MBNV3XdGiwa4xlf94v2kiwGdzJWRCDdGDPpZF2GorRRV6653xlU5YcgUEfAzY/wHoDXKjaULUqtFz03ljImuANDbKm9enxrPoMphRAxrOqIAgDMTch7FmwOaH3HD2nbcsLYdAPCGhzlPPzlwHuemc9ixth0vHB3D8dGU9FnBZKYoHeEQlxYkDNDnHSk+13LVgJ/V5coFwYB7KilfrjaN7Aa0PgZgdqkkQG5ZT6ZgHTFEZVJJRZuIQbJz2ipiELOW3CKG6ZxYEFR/vj0axJRE5/REuoCOaNBIBQFAdyIEzt2rmrJFLbdvjhj6WrV+CpkhfsdGteqljfoOibW6MJyW9CgODCURCypY0x7Bxu4YFB/DkRH5HoqfHhhBdzyIr350GxgDnnzLWyrqucPnsePBZ/Cuv34BYyn5bXvEpQEJg07Q73OtSrKKFgC989nhrJjOGbIyrhWJclVhPqsWwuKSSipXqiiUq9Z9DPo+h6rD5FCRSmrsY6ilktwihlJdD4OgJRxwNZ+NiKHhfFskYKwbdWIyU0R7tCHakKxqOmdUJJkihhb5fRAnRtNgDFjfFTXuOR5ScFpyydDBoSQuXxGHz6e9aFnXGTUGArpRrXK8fGICt2zqRE8ihCtXJvDKyXGps4Dmb/zXHx5EUPHh3HQOD714QvqsoFiuelrfSiwtSBh0tIjBYSRGuWppPIuzTiG3WN1pFTHI9DHkSxX4mHUaK6I6D+HLlkQfgnUaivPaLCYrMoUy/D7WlAYTqSS3fLuV+QxoPoN7xKB9vCXSKAzanCa3fdXjmWKdvwAAXXofhFvntIgKzBFDdzwIv49heNo9lXRuOoeeeMj478sYw7rOKE5LppLOTGYNUQGAzSviOCwpDKcnMpjMFPG2dVoK6m3rOrDn7LTrMinBrjNTOD2RxZ/fuxXvu2oF/nXPOU9jx9OFMt7/lZew/S+ewcMvnZQ+RywdSBh0VMU5YiiUK5alqoDwGKq2Nf0Fm3JToGYoOze4abOOzCkRQURVHFNJtTlL1qkkwLmyKJ3X5iQ1fm9jn4NDxFCpcqQK5aZUEqBHDC6iMqOP9W6xiBgAd/N6MlMwNsYJjIjBJT0yqn+8J1Ebx6H4feiJB6UihpGZPFaYRnkAms8gU+6aK1YwlipgdXvEuHb5ijgGp3JS3eZvDWplsVf3twIArlnVimJZG+8hw88Pj0LxMbx7Sw/ed1UvJjJF7Dkr34Px0AsncGw0jbUdEXzx6cOeG/RyxQoe2zWAQx7HjxDzBwmDTkAmlWQTMQQVHzgHSjYehRExWI7E0K45mc9ZiyU9As1jcH7FD1hHDFExUsNhLEa6UGlKIwFATFXAmPOiH+E/WKWSEhJD+KazJURUf5Mgi07oKZd9EOaVogIhDG4Rg8ird8Xrz8suChqayWFla70wrO2IYHAq6/rKfWBKE49VJmHYvCIBAFLppP3nZhBUfNikG99b9HEesg/al09MYNvqVsRDAdy8wdvmu0qV49GdA3jX5d345m/fgFKF4192DUqdBbQ01v3/sAt//PhbuPdvf+m594OYH0gYdFSXQXjFipMw+I3PscIpYpDpY8gXm/c9C9yEIesQMYhrTg1yVgP4AH0In6o4ppJqI7ebv7dMxNDY9SwQ2+ScfIZcsYJssdLkMUSDCsIBP8ZTzqIyliogHlKafu8rWkKu01k551rEkAjXXV/VHkGVuw/xOzvRLAziIS+zT+LEWBrru2JQ9NTj2o4ogopPagBgpcpxeCRpRBttURUbuqLYfVouYnhzYAqjqQLu3daH9V0xXN3fgucOj0qdBYAXjo7hpWPj+MxtGxALKvji04elzwLAaDKPD3/tl7j5C8/hxaPeR5AQGiQMOupczOeA6F62fkAXnCIGmVlJFvueBWHVuVy11qBm3eCmfY7D+WLzkh6B27ykGYslPYJESHFtvNJ2TatN1w1hcKhMmtB3SnfGms93xd37IEZT+aZoAdDKXUeSecdRIMl8GdliBb0NqaR+3a8YnHJOJ53V+xXMqaT+tjAUH8MpCfP6xFgGG0z+hOL34fIVcamI4cxEBvlSFZeviBvXrl/Tht1np6R2YLxwZAx+H8M7N3UBAG67rAtvnJ2SbrL7/hvn0BoJ4A/vvAyfvHktXjo2Lm3YA8Aff+8tHB7WoqoHvrNHeu+H4MWjY3jgO3uM4YfLFRIGHVVxHmtRsCk3BUx7n23Oi4e+lUfh92mrQd36GJxSSU4b3IRoWJ0XvQ1OEUMq37yLQRALKY7lqimbHghAixhShbJjRdRMrmgdMUS1a06pJKO5Ldr8cO+MufdBjKUKdVNdBT2JEPKlqmP/hhi50duQSurX90KIGUx2nJ3MIqL66/wRxe/D6o6I60MyX6pgYCqLDXqZrOCK3gQODSddH+6H9IfqFb0J49r1a9ownS0ZQwWdeGNgGpt74kbBwDs3d6HKgZeOu796zxTK+OmB83jfVb1QFR9+5bp+AMBPDsiV2u4dmMbzR8bwh3duwrc+eQMyhTK+9ctTUmcBYM/ZKfzOt3biZwfO448efwvf2y2fAgO0CPlvnjmKL/3s6EXfbU7CoKMqPsemp4JDxKC6CEPBoSoJEHufnc1nu1SSKDm1+wdv14egndX3OThFDBZLegTxUACpgkwqydpj4NzZo9Amq84ulSReKbZbRAydMfeIYSxVQFc81HRd7IZwSieJBrjGiGFFSwiMAYMuHsXgVBar2yNNhv/6zqhrxHB6IgPOYXRcC67oTWAqWzJMdTsOjyTh9zGjMQ8ArlvdBgB48+y041nOOd4anME1q1qMa9f0tyIeVPDyiQnHs4D2aj1XquBD16wEoPk5W3oTeFYyFfX47kGEA3589G2rsaknjls3deF7e845vvgw84WnDqMzFsTr/88d2L6mDV94+rB0g1+5UsUn/34n/uaZY/jKs8fwW994zVNzIOcc3915Fp999A08+daw9LmFgoRBJ+hSleRsPmsPbbv/EZwiBkBLJ7mVqzqlkji3N6/FQ9967LYeMTg8nK32PQvcUkmis7mxqgioiYVT9/N0roSWcPODPaL6ofp9jqkk8eDvtIoY4kGMuzS4jdpFDPo1J2EYMYSh3mNQFR9WJEJSqSSzvyBYpwuD04PuxKgmHOZUElDzKNwqkw4Np7BeH/wnWN8VQyjgw4Eh51TUmYksZnIlw58AtEjn2tWtrqICAK+dmkQ44Mf1a9qMa3dc0Y3dZ6Yw7VJowDnHz4+M4uaNnUaPza9c14dz0zm8dsrdOB+cyuL105P42E1r0BpR8Yd3XoaxVAH/9sY517OAJkq7z0zhS//uGvzdx67HvnMzePgl+Wjly88cw//9vX147tAoHvjOHvzDIg9NJGHQUf0u5rPNBjbAlEqyeTiLiCFkGzH4XcduWz3YAfOyHusHtBExWDa4uZvPVms9BbGgcypJpFvsIgbAvuSU8+bJqgLGGNqiAcdUklvEMJUt2vZBZAqaR2DpMehRgJOBPDydg481VzQBmldwziGVxDnH2clsnb8gWNcZQ6FcxbCDKJ0Y0xvrOusjho3SwpDE5aY0EqClO7f0JnBgyLlCaO/gNADg6v6WuuvXrmrF4ZGka4f+qycncP2aNmMHOwDcfnk3KlWOl445N+idGMtgcCqH2zZ3Gdfes2UFoqofT+wdcjwLwHiV/sGrtWjl5o0d2NKbwLdePuN6tlCu4MvPHMW21a348LY+vPfKFbjj8m48/NJJ18kCAHBgaAb/67lj+NXr+rHnv7wbt23uwoNPHZKqflsoSBh0XMtVJaqSZuMxAFr38uzNZ+dlPUZVkmWDm/NZzrmjMMRDAcdcu6hYatzlAJjmJdlUJmWLFZQq3NJjALR0klMqaSJTRFDxWZruXTEVnMPWmBTpFjuPwfw5VgzPaMZ1wCL12NcadvQYxtIF5EtVS2FY26ldc9oJcXw0jb7WcJOn1BUPIhFScMxhZlIyX8K56Zyxrc7MlStbcHAo6Rit7B2YQSjgw2U99ee3rW5FlQP7Bu2FZTpbxJHzKezQm/IEV/e1IBZU8MpJ51TUC3oF0jsvqwlDWPXjnZu78Nzh867ppB+9NYyr+1uwukP7HTPG8JHt/Tg0nHSdM/XMwVGcTxbwB3dsMtJ/n7l9I6ayJTy6093E/rsXTiKqKviTD21BwO/DX9y7FQDw35465Hp2oVhywsAYu4sxdoQxdpwx9rkL9X1lGtzcqpLszrtHDC7mc7FqLPRpREQMdhGH6Fy2Hv7nR8DPbJum8qUqqtzanwC0yiLHctWcJip+i/lStZ0M1udF17NVxADowuBUlZQuoiOqWjYFuvUy2PUwAFp01xIOOEcMM/mmNJKgvy2CkWTeNloRE1RXtTefF1HAKYctcifG0k3GM6A96DZ2x3DMYTWp6JG4YkWi6WNb+xJIFcpGxZQVbw1O48qVLU2CeO0qLTXkNARw5+kpcA6jW1ug+H3Ysa4dr7p4FM8fGcWGrmhTCu7OK3pwPlnAfodo5/R4BvvOzeADV/fWXX//Vb1gDPjhXuec/7/sHkBvSwjv2FQTpevXtOH6NW34h1dOO4rS0HQOT+4bxn07VhmRdX9bBJ++ZT2efGsYhz3Mx5pPlpQwMMb8AP4WwN0AtgD4DcbYlgvxvd2Ewa3BDbD3GGrlqvYeg2Mfg0PEYKSDbB7u2r5n665pQO+ctjlbm5Nk/b1jQQWFctX296YN0LMTFedlPdNG13NzKgiAayppIlNoam4TdMbFvCTr807CAAA9iaCL+ZxrMp4FfW1hVKrcdu+0Vamq+fuGA37b6qBqlePkWMZSGABgU3fcsQ/isF7OerlNxADA1mcoV6rYPzTTlEYCgPaoijUdEUef4fVTE1AVH65Z1dr0sbdv6MDJ8YytGOeKFbx2ahK3be5u+tjtm7vhY8AzB8/bfu8n92kP/vfraSRBdyKEG9d14IdvDdkWd4zM5PHi0TH82vX9TS+APn7TGpyeyOIXx+3TYI+8fBoA8Ns3r6u7/ulb1yEWVPDVZ4/bnl1IlpQwANgB4Djn/CTnvAjgUQD3XIhv7NrgVq46jMRwTiWJ/gb7qiS/bQ8E51wqlWQ3Lylrs71NEAsqxpa2RjI2uxgEbst67AboAbX5R3Yeg90uBkFrRDWG7FkxkW4eoCfoEhGDTTpoTB/h0G1RlQRo6SQ7YeCcu0QMopfBOp10dqK2TrQRMW/JrjJpJJlHrlTBugbjWbCxO4bxdNE20jo4nEJLOIAVieafe1NPDAE/s33lfWw0jXypimtMxrOZbatascehF+K1U5O4dlWrZfXdjes7AMB2EOCrJydQLFfr/AVBW1TF9jXt+Nkh+8qmH+4dwnWrW+vmYgk+eM1KnBzL2DYHfm/PIKoc+LXr+5s+dtfWFeiIqvj2K9Y+RbpQxndeP4v3XdXb9L1bIyo+efNaPLlv2LbbXXaE+2xYasLQB8CclBvUr9XBGLufMbaLMbZrbGx+uhulGtwchugB7hGD1XRVQEsl2UUMpQpHpcod+xgAZ4/Byng2n7czBe0mqwrclvVYjdwWiJEadh6DWyqpPaJiKlu0DdMnLQboCWoRg40wpAtQfMzW39CEwfqsXXObQDzw7QzogaksehJB2/LkdV1R214GIRgbOm2EoUc3oG2ihsMjSVzRG7eMLoOKH5u647YRw1s2xrNg2+o2jKYKlrssMoUyDgwlm9JIgi29CbSEA3jFJp30/JFRhAN+Y29FI3du6cah4aRlNdjx0TQOj6TwgYZoQXD31hVQfAw/eLPZwOac4/Hdg9ixrt3Yt2EmqPhx345VeO7wecvv/djOAaTyZXzqlnVNHwOAT92iRQ1fefZY08cGp7K480svLNiQwqUmDFb5jqZ/+Zzzhzjn2znn27u6ml8lzIbgnEZiOFcl5UsVMFZbCNSIZj5bn7Xb9ywwhMFGWHJF++Y4QJuwarf32V0YnAfppfLNS3oEPh9znLBaG7lt/XBvjQRQ5dbfm3OO8XTB8BIaiaraPgi7QXpjKe2s1e4NoLbsx2riqEh3NA7QEwjBsI0YbCqSBOs7oxiYylm+iBEpJruIQZSsWvkM1SrHkZEULrfwFwRb+xI4cG7G8lX/3sEZJEKKsXeikW2rWwEAb1ikk944O41KlWO7zYPd52O4cX27rQH9wtEx3LShw/bfyJ1X9AAAnrWIGn701hAYA97f4C8I2qIqbtvcjR+82Txhds/ZKZwaz+AjFtGC4KNvWwMA+M5rZ+uuV6oc3/zlKdywtg3XWqTPAC1q+O23r8VT+5ujhq8+exwMDO+7yvq+58pSE4ZBAKtM7/cDcK81mwecqpKqVY5ShTvsY3BvcAsp9nl+pz4GY62nrTCIJjX7clXnVJL9Fje3VJLbhNVkvmREFVYkwoqD+Wy9pEcg0kSTFj5DtlhBoVy1TSUxxhyb3LTmNmtRAbRcf6XKjZ3SZkTXc+MAPUEo4Ed3PIhz09Ym7oBND4NgXWcUlSo3Bu2ZOTWWQTjgt0wFAcDKljDCAb9lZdLZySyyxYplRZLgypUtmMgULf2RvQPTuLq/1VZML1+RQFDx4Q2LKa07T0/Cx4DrdPGw4qb1HRiYbF5veno8g9MT2bpqpEbWd8WwvjOKZw7V+wycc/zorWHcsLa9bopuIx/e1ofzyQJebRCmx3cPIqL6HR/Ofa1h3HFFD767c6Auo/DUvmEMTuXwqVvW254FtKghEvDjK8/VooZDw0k8vmcQH33baqy0SH/NB0tNGHYC2MQYW8cYUwHcB+CJC/GNVcWHKodltYiIJGwjhoB7g5udvwA4m8/G9jaLJT2AeypJixicUkn2W9zs9j0LEm6ppFzZ1nwGtMokJ48hFPDZvgqsdT83C0NtHIa1MACi+9nGfE67CYPofrYSBhEx2P+D7WuzLlnNlyoYSeYdI4a1eprIqmT11Hga6zqjti9AfHpHs1Uvg6h+uaLXOWIAgAPn6tNJ+VIFR0ZStmkkQPu3c1Vfi2Vl0s7Tk7iiN+H4IuLtG7Upr41Rw/NHtCjAyl8wc+eWHrx6cqLu/9Uj51M4PprGB22iBcEdV3QjHlTwr3tqzW7ZYhk/2juMu7f22v77EHzsxjWYyBTxlG5ylypVfOlnR3FZTwzv3tLjeLYtquK3b16Lp/YNY9/gDPKlCv7o8b1oiwTwB3dscjw7F5aUMHDOywB+H8BPABwC8Bjn/MCF+N7ioW+VThLX3BrcbMtVS/bNcYAwn51TSa7ms42waB6DfcQQdZjOKobrWc06Ml+3ihiqVY5U3t58BpyFYTpbsk0jAbVIwqojVgzQs/MYAOexGGOpgmFQWyGEweqV8/BMHj5m3QMh6G+LWArDuekcOAdWWRjPgvVCGCx8hlPjGds0ksBOGA4Np+BjWuWSHVf0JsAYmgzog8NJlKu8ruPZim2rW7Hv3EzdC6hSpYo3zk7b+gOCTd0xdMbUprLVZw6NYn1n1DLHb+bOK3pQqnC8eLRmYD+2cxABP8PdLumYUMCPD167Ej/cO2Q0nT3y8hmkCmX85o2rHc8CwC0bO3FZTwx//ZOjmM4W8fBLp3BqPIP/9J7NlqXcjfz7W9ejJx7Cbz78Kj7w1V9g/7kk/uLeq2wj4vlgSQkDAHDOn+KcX8Y538A5f/BCfV+RJrJ6uItrdhGD4mPwMadUkv2sI0Azn4v6+s9G3DwG1e+D38dsDeSsi8fgtPc5rc9Bsk0lBe23uGWKZVS5ddezIOHQIDeds+56FhippEzz93YaoCfoilsP0qtWOcbTRceIYYXDvKTh6Zxtc5ugvy2M4Zlc039vo1S1w14YWiMq2iKBppLVYrmKgamcIRx2bOyOYXgm3/Tf7NBwEms7o85+lKpgfWcU+xsihrf0KMA8I8mKG9a2o1iuYveZWjrp4FASuVLFVRgYY3j7hk48f3TMmGk2mSnilZMTuPuqFY5nAS1N1RFV8W9vaq/6c8UKHt89gPdeucLWizLzwO0bAQBf+ulRjKcL+LsXT+C2zV3GHCknfD6G//4rV2MsVcA7/vLn+OLTh3H31hWu0YKgNaLiu797I3as60AsqOBrv3kd7trq/jPPBecYaBmhOrzqFw98O4+BMea49znvEjGIaCBfqjQ9hPNF54iBMYaI6rcdne1WrhoNKrYjMUQZa8Tme4vQ36pcNWUs6ZldKmk6W7KcsSRo1VNJThGD0yuqzlgQk5kiKlVe96ptKqtdcxKGjqgKH7MWhpFk3jGNBGh551KFYzRVX9Y64NDDYEYrWa1/1T8wlUWlyrHORRhqex0ydabnweGkbampma19LdjZMHtoz9lpdMeDtt6G4KYNHVB8DC8dG8fb9QVALxwdA2No6ni24kPXrMQTe4fw4tEx3HFFD35yYASVKsfdW90NWMXvw307VuFrz5/A4ZEkXj0xgWS+jN+6cY3rWUD7b/apW9fh68+fwNP7h1Gucnzu7sulzgJaw9s/fvpteOSV09jYFcNnbt9gm/KzYk1HFA9/Yrv058+VJRcxLBaOqSSXiEF8zH4fg1vEYL+TwUglOb6Ss9/7LFOumi9ZRyuZQhlR1W9rKKqKD0HFZ5lKEmWoTnljR48hV3KMGBIhraPaaqzFhH7NLZVUtRiLIbqhnYRB8fvQFbduchueyWOlTUWSQPQyNJasDkxmEVR8jmksQJuZ1JhKEp6DmzBsNCqTagb0ZKaIwamco0cguHJlAkMzeeP3xjnHKycncOP6DtcHXTwUwHVr2uoW6PzkwAiuW93m+PsWvHNzF9qjKr63ZxCca5vi1ndGceVKe1/EzKdvWY+WcAAf+8br+O8/PoxbNnbalsha8Z/esxl/9N7NeMdlXfjHT7/NsYLLih3r2vG3H70O/9e7L7PtiVoqkDDoOPkERZfOZXF+thGDGJVh5RO4eQyA3r1scbZS5SiUq46iYizrsYgaMoWy5ZwjM/GQYpkOEh3NjqmkcADFctVSEN08BsYY2iIBy3lJE+kiwgG/5dY6QZdNL4Nb17OgJxHCSIP5zDnH8HTOtlRVYNfkJqaq2gmxYH1XFOeThboUoBAKN2FY3R6B6vfV+QyiB+EqCWHYqndA79NXbp4Yy2AsVcBNGzpczwLaLKMDQ0kMz2gVRgeGknjvlXIplYDfh49s78eP94/gc9/bh70D0/idW9ZJv/Jui6p4+OPb0R0P4sb1Hfib+6719Krd72N44PaN+PpvXe+a+rrYIWHQETnh2UYMwYC9MMhHDM3nRSTgdD4csF7WI3wHp1RSxGEnQ8ph5LYgHgpYppKSxvY2+/MJh3lJbh4DILqfmyMGp+Y2QadN97N43y3v3JMIYbQhYkjmy8g4NLcJ+lrFwp760sszE1msanMvPxQP/9Omztfjo2m0R1UjxWaH4vfhit54XT/BW/pwu6v63IXh6lWtUHwML5/QTFxRJXTTejlhENNL//m1s3hM35J215XytfifuW0j1ndG8d1dA7hpfQfuu2GV+yET29e248k/uBWP/M4OKW9huULCoONoPle0h6ajMCh+h3JV96ok7fOaz+clU0lWHkOt1NX+4Rx12OLmtKRHELcZpOe0pEfQYjN6O1+qIF+qGmMz7GiPqJappPG0/ZwkgVj5OfuIIdhUlSQe9FbjLMyEVT86Y2rdWOVqlePUeAbrbeYcmRFNZOZ00oHhGemUyg1r2/Hm4LTx/+tbgzNY3xV1TPsJYkEF29e24dlDo+Cc47lD59HXGsYaB8PczOqOCO7eugJfee44vvrccbz/ql5Hs72RlnAAP/oPt+L7n3k7vv2pHcZea2J+od+qzlzMZ8B50U+hXHFMQ0l5DE6ppKB1KkmUoTqXq9oP4dM8BhlhsDef7UpdAXthEO87pZIArWTVal7SZKbo2MMA2I/FGEsVEA74HX9ngNb9PJ0t1f03E6khp3JTQeP47XPTORTKVdsBeGYax28XylofgRh058aOdVp10FuDM6hWOd44O4VrJYxnwQevWYnjo2nNCD42jg9es9JTSubP7rkSd1zejds3d+HP9RHTXgirfmxb3eZY+UXMDfrN6jgJg1Qqyc1jcGhwCzumksTIbgdhsE0l2W9vM84aW9yahSVdaK6SasRuWY9IDzl2PoesdzKIpjW3VFJbRLXsfBYjt52IBxWoiq+pyU00t7k96LrFXgaTzyCqivol0kH9bZE681lMPd3Y7S4MEVVBb0vIiBiOnU+jVOFSqSAARn789VOTODCUxESmiFsv65Q6CwD3XNuHrngQn330TQT8DB+/Sa6yR9AdD+Ebv30D/v6TOxa0Fp+YPVSuqmMMwnPwGJzSQUHFvkmt4DCZFaiZz3YRg6r4HBthIjZNasJjcEwlCY/BQljShRLiIfuGJ0Df+2yTSgoH/I5iahcx1OYkuQhDVPMYOOfGg5xzjolMwXJzmxnGGLpiwaZ5SW7jMASiNPN8Km+kQgancogFFVdBA7Tu558d0hbI+HwMJ8asV3Lasa4zihO6MOzXjWDRmexGW1TF1r4Efrx/GFOZIhQfq9sl4EYsqOChj12Pb718Gvdu61uwsQzE4kERg45IE5UsPQbJclXb6aoV2yU9QC1isKpKyjus9TTO2wqDRCopaD86O1OoGB6EHXappGTOfoCewBCGrLUwuHkMbZEAShVeNwQwVSijVOGuEQOg+QyNy3rOJ/Ou5aJArcnNPC10YDKL/rawVFplVVsYxXIV5/UR3yfG0miLBFy9EcGW3gQODSeRL1Wwd3Aa8ZDi2v9g5r4bVmP/uSQe/sUpvHfrCunvK9i2ug3/875tuN1iBwJx8UPCoBN06GMQkYCbx2C/j8EtYrD3GLLFsqO/AGgPd6tX/Nmiu3EddVjvmZapSgoqSBfLTeOvnUZuC4yqpAZhEakkp85lwDQvyWRAi9SO3S4FM43zkjjnODedQ59UKkj7HPNQt8GpnOMAPDOb9PWXh/WpmcdHrTev2XHzxk4Uy1W8fmoSzx8Zw9s3uPcRmLnvhlX4yPX9uGl9B/7LBy7ILiziIoKEQSfgWJUkU65q3flcrXIUK1XHiCHomEqqugqDGNvd+HCulas6VSVZm89FfTNbzNV8DoDz5qqmVL7saDwD2u88ovqbUkmi0sjVY4g2D9IbNZbsuL8C7orXz0uazBSRL1UtF7Y0ElEVdMWDxrIUzrWJpzL+AlAbVndoWNujfGg4ictWOKftzLxtfTviQQW/+w+7MTyTN0ZLy6L4ffirj1yDf77/RsfJosTyhIRBR8Z8dvYYrDuf3dZ6Am7ms3MPBGC/91nKfA5Ym89CKGQa3IDmQXpJlwF6gtZwc2XRZKao70xw/rnbdOEwN7mJctPuhLswmMdiADDKR2UiBgBY2xHB6QktYpjIFJEtVqQqkgAtjba6XVt3eXwsjVS+LDV3RxBRFXzspjXIlSpY2RLCh661XjRDELOBzGeduY7EsFv0I3yHufQxOKWCgNqDP1OsT/3kJIRB8WtjLRpTUW4jtwW1LW4NwpAr2S5tMdMeUzGZqc/zT2aKruYxUIsYzHsRRCqpSyqVpKJS5ZjMaEPzRJWQTMQAaP0EPz+ijXc4qo+Y2NQjnw66aX0Hfrx/GL84pjWLXb9GXhgAbUTDlpUJ7FjbvuRHLBAXFxQx6DhGDDKpJJuqJBEFOL36Dfh9UHzMdiSGaypJT/c0zkuqRQzuJaeNqSDxvluDW8zY+1z/qj/psL3NTHs02NSkNpkpot2lgxew3oswmsojqPgc90AIenUBGNIjBRExyKaDNq+IYzxdwHi6YGxF29wjnw565+YuJPNl/NcfHcTmnrjrOItGfD6GD1y90iidJYj5goRBRxjLVj6BVIObzUgMmYgBEFvcZpdKElVHjQZytlh2LXUFtF4Gu1SSe8QgehFqwsI5RzLnbj4D2qTSiQZhmMoWperbY0EF8ZCCkZlaP8D5ZAHdCfc+BKDWiCa2oQ1O5RBV/Y5TXc2IIWpHRlI4NJxEayQgVeoqeM+WHqOSyG7vL0EsBpRK0nHbx6D6fY4PG9WvpZJEXbpAiIXbwz0U8NmWq7qlksK2wuBe6gpovQyN5rNIDblFDAkLjyFfqqJc5VIjFtqjzWMtJtJFqUYvQNuhbB5NMZrKS1UkAcCqdlFZVIsY+iTLTQEYIyj2nJnCztOTuG51m6fKIMXvww9//xYcGkl6mvJJEAsNRQw6Ph9DwM+MJSBmiuWqYxoJqFUWNfoMwjeQiRiszGstleR8NmLTpOY2cluglbvWf2/hMbhVFsWCzes9ZTuXAU0YssVKnb8ylZVLJQHaCs2RGbMwFKQqkgDNH2mLBIwFOYNTOWl/AdA8jitXJvDozgGcGMvMauJmSyQgNbKaIC4kJAwmAn7reUfFSsVdGHTzr9FnkI8Y/MhbNMjJeAx2e5+zxbJrtCHONza4GYt2XF71C+Ewj8UQwtAmIQyiEU2kk/KlCrLFipT5DAArEsG6JrOxpLwwANoIimPnUyhXqjg55q2XAADed1Wv4U188Br5KaEEsZShVJIJ1a6yqFR19BeAWkRQqFQA1B6IRsTg8qo/FPBZLtvJFSsISVYlWZnPsqmkxqUztVlHzv+LRFQ/fKw+lWSMtJB41W+s6EwX0dcaNtJKXiKGsXQBpUoV5QpHqlD2ZMZe1hPHE3uHcHoig0K5ist7vS1f+eTNa3F6PIMb1rW7TlUliIsFEgYTqm3EIJFKEsLQGDGU3HsggFqTmpmqWLTjGjGIVFK9MORkhSGoNJnPyXwJfh9zPc8YQyyoWKaSZAxksTdBrOMUwtAmOVyttyUEzrX+BfHzu+1DMHN5bwL/9NpZPL1/RHvfQ5MZoP3u/+oj13g6QxBLHUolmVBtRmcXy877FACt8xlormoS6aHZpJLE++7lqiKV1OAxlMqupaqANhbDrnNZJvcdDwWQMqWipiQ7lwGtXBWoCYL4W2bWEVA/s0iMp5DdDQAAN+qm71//9ChaIwGjI5kgljMkDCZUxWc7XdUtYqiVu9Y/3GUjhlCgeW9zTmLWEeDgMRTcK5q080rTBjfZclOgeZDeVFZunwJgSiXpgiBGVMiOY+41hCFnjKdY3S7fD7CxO2YYzu/a3O1a2ksQywESBhNzSiUFrPsgvJjPjWdF+arb2YDfB9Xvsy5XdTkLALGgH8VKte5nl5l1JEg0jN6eyhYR0/cduJ9VEPAzw3wWpadue5MFq9sjYAw4OZbBmckswgG/sZ1NBsYYvvab1+Gea1fi8++7QvocQVzKkMdgIqj4LMtVC2UP5nNpluWqSrP5nJfY3iYIq83LerJF9+moQH25q6poD1WZ6aiCWKjevJ7KuO9rFjDG0BZRjbEW52fyiIcUqRSYuPfV7REcGUlhPF3A5hVxz6Wf16xqxf+8b5unMwRxKUMRgwnbclWZPgZRrtqYSpIYogdoD/ZGj0Fsb5MRBqtlPdmiXCpJNLGZ00EpyZEWgHUqyctmrt6WkFFyOpLMG0twZLmsJ44DQzM4MJSU3mJGEIQ9JAwm5mQ+28xa8tLg1jhEz9j3LPFwb1zWUyxr3ccyqSSxEMc8/jqZK0l1LgOaH2DeiTCdLUqVqgr62sLGvKKRZEE6jSS4cX0HTk9kkS6Ucd2aVk9nCYJohoTBhF0fg4zHEHLwGFS/r25MhuV5xYd8qQrOazsVZD0GQEQMtVftxi4GiVRSq8WKzWS+LJ1K6owFkSqUDWGbypakmtsEK1vCGJrOa4typrJY2eJtVeT7rloBQPMr7rqSmswIYq6Qx2DCznwulCsSHoNNuWqp4trcBsBoYiuUq4YQCM9ALpVUP9ZCpHZkDGTx6l40plWqHOmCvPlsrixa2RrGVKZobFeTYWVrGLlSBQOTOYyni1jrccpob0sYL3/uXShXuFR0RRCEMxQxmHBKJbmWqyrW5ap5iZEWABBSmncyiKYzt0F2gBYxmIfwJfUqIZnx08Ions5p6SAx3kJm0Q5gGmuRLqJUqSJVKHsSBjFu+plD5/X3vXcQr2wNY7WH/gWCIOwhYTCh2uxt1jwG54e7XVVSTmI6KlDzEcwP91o6SC6VZJ6QWosY3B/uYsy0iBiEqMhGDGKR/ESmYHgN7VH5VJJoKnti7xAAYF2nt3lFBEHML5RKMmFXruqtKqk5lSQVMRh7n2vnM3pqSGZCajig1JW7ekklhQJ+hAI+w2OoRRuyHoMWHYylChiJatVFXvYI9ySCaI0E8ObANBIhRXrkNkEQCwNFDCYC/tmbz3appFypaozLcEKkkswP92yhDMZqouFENOhH1hRtiI1qspVFrWEV0/qMo9pkVbnXDUIERmbyRtlprwcDmTGGd13eDQDYsa6Duo8JYpGhiMGElflcrXKUKtzVfPbr+xyaylWL7vsUgJr5bO5lyOj7FGQathrLVWUX7QhaIwFjlEVtsqqcqIQCfnREVQzN5A1foqdFfvQ1AHz2jk3wM4bP3rnJ0zmCIOafBYsYGGN/yhg7xxh7U//zPtPHPs8YO84YO8IYe6/p+vWMsX36x77CLvD2EivzWWbfsyCoNI+1yJdnbz5ni2Wp6agAEAkoWu+Cfr9eUkmA5jPM6MJgTEf1MFpiZavWizCSzEPxMXRGvQnDmo4o/uoj19DoaoJYAix0KunLnPNr9T9PAQBjbAuA+wBcCeAuAF9jjImn39cB3A9gk/7nrgW+vzpUxYdylaNarfUSCGFwa1ATn9OUSpLY2QzUzOfGqiSZkRaAaZCefj6ZL0H1+6S+NwC0RVSjKmk87W3CKaB1L5+b1gbZ9bWFXfs2CIJYuiyGx3APgEc55wXO+SkAxwHsYIz1Akhwzl/hWpfXtwHceyFvTEQFZp9BRBAyEYOq+KyrkmZpPnuJGMINy3q8DMEDtFSSqEqazBQRUf3SogIA67tiODORwYGhJC7r8bbTgCCIpcVCC8PvM8beYox9kzHWpl/rAzBg+pxB/Vqf/nbj9QtGbXR27eEs3nbzGAARMTRXJbltYAOszedMQW5nM6CZz0Bt9LZXYWiJBDCdK4FzjslM0dOsIwDY2pdAqcJxZiKLy3qoqoggLmbmJAyMsWcYY/st/twDLS20AcC1AIYB/A9xzOJLcYfrVt/3fsbYLsbYrrGxsbn8CHVYzTvyEjFoHkNjg1vVeOg7EbYwn7PFslQPA6CVqwIwehlSeflZR4BWlVQsV5EvVTGRKRq9CbJc3ddqvH39mjb7TyQIYskzp6okzvmdMp/HGPs/AH6kvzsIYJXpw/0AhvTr/RbXrb7vQwAeAoDt27dbisdsCOhRQckileTW4AZoOxnMEQPnXG9wk6hKMszn+j6G/jZvHoNokJtNKgkAJrNFTKQLnvoQAGB1RwSfuGkN3hycwTsv6/Z0liCIpcVCViWZp5l9GMB+/e0nANzHGAsyxtZBM5lf55wPA0gxxm7Uq5E+DuAHC3V/Vqhzjhjqq5pKFY5KlUt5DEHDY6jvY5CuSlIbU0klT8LQk9AihPPJPEZm8sb7Xvize7bi3z7zdupDIIiLnIXsY/hLxti10NJBpwH8LgBwzg8wxh4DcBBAGcADnHPxNPw9AN8CEAbwY/3PBcPSfK5U6j7mRFCpn1cku+9ZO+sDYw3CUKp4EAbtP6UYvJfOlz2lklbq6y1PjmUwkSka6y69coErjAmCWAAWTBg45x9z+NiDAB60uL4LwNaFuic3hMFcnIP5LEo+Aa25DZATBsYYQoq/IWKoSI3NBmoRgxi85zWVJIRh95nJuvcJglh+0EgME7WxFvNTrprzsJoT0Ndz6meK5SqKlSqikhFDi2mnQrXKkS56ixgSoQDiQQU7T08BIGEgiOUMCYMJK4+htppTLmIwVxUJI1m2H0Db+6ydEWWrsruPE+EAfEzrWk4Xy+AciEtGG4J1XVEcH00DANZ73IlAEMSlAwmDCSOVZPIY8h62qIVVf11VUW01p9yvORpUjFHbGf3vqGS5qt/H0BpRMZUtGqOv2zz2Ily3WiszXdkSQrfHqiSCIC4dSBhMiIihVG4WBpmdCqGA3/AVgNqrftmIIRZSkNb7EIxdDJIRAwC0RQKYypSMkRadHmYdAcBtm7sAALdfTuWmBLGcoemqJqyqkox0kEQqKaJqo68552CMGWklWY8hHgoYk02FiSwbMQDais3JTBHj6QIAbRezF27b3I19f/oe6YmsBEFcmlDEYMKqKslTKingR0Uf0w14q0oCNE8gpS/JycwqYtBSSRNGxOC9FyEeClDJKUEsc0gYTFiZz14M5LDRS6AJgteqpFjQlEoqCPNZPmLoiAUxlipgQo8YvM47IgiCAEgY6jDKVSv1BrLq90l18zaOpch58CcA3WPQ9yh4Xa8JAH2tIUxkihiYyiIRUqRKbAmCIBqhJ4eJoF97gDemkoISG9iAWmQgjOOaPyEfMWSKFVSq3Ni/LDaiySCW3Pzy+ATWdFC5KUEQs4OEwURA0aKC+j4GuUU7gGkngh4pGP6EZLmq6FTOFMs1YfDQvdzXpjWlnZvOYS31IRAEMUtIGEyoFtNV86WqsUTHDRExGB5DsQIfkxunAdT2M6fymjDEggoUybMAsKa9thZzXQetyCQIYnaQMJhQ/D74WHMqSdY8bvQY8iUt2pCt8hGjr2eyJSRzZWPMhSzmprTraCcCQRCzhArWG1AVX10fQ64kn0oKBepHX2eKZc/lpoA21mImV/LkLwi+/OvX4OXjE3jnZV2ezxIEQQAkDE2ofl9TxCBrHouIQXgL6UIFMY8NaoC2czmZK3nyFwQf3taPD2/rd/9EgiAIGyiV1ICq+Oumq+ZLVemqJBEdiK7lTKGMqIcu4lZTxDCdK3pOJREEQcwHJAwNNG5h8+IxxEL1e5fTnoVBX6+ZKWI0VUD3LLaoEQRBzBUShga0vc3m0dnyHkMk4AdjQEoXhkyh7GnuUMDvQyKk4HyygOlsCT1xmnBKEMSFh4ShgcYtal7KVX0+hqha6172mkoCtLEWB4dmAIAiBoIgFgUShgbMW9QAbW+zbMQA6N3LRirJm/kMAP1tYewdFMJAEQNBEBceEoYGwgG/0aAGeEslAdqY7LQplRT1UK4KAGtMjWmUSiIIYjEgYWggFPAjp8844pzrqSQPEUMogHShjEqVI1eqeE4lrWmvjbLY0E1jLQiCuPCQMDSgrefUIgZRtirrMQBATI8YxD4Fr0tvRMdyUPEhKNk/QRAEMZ9Qg1sD4YDPEAZjCJ6HB3QsqGA8lTU2sXntRbh+TRv+/N6tWN1Os44IglgcSBga0FJJQhjkl/QIovqynemsLgwR701qH7txjeczBEEQ8wWlkhowm895Y9GO/K+pNaxiWp91BNTmHxEEQVwskDA0EApoIzGqVY582XsqqSOmIlOs4HwyD6DWzUwQBHGxQMLQgFi2ky9XjMjBSypJRAinxjMAgFaad0QQxEUGCUMD5mU7wmOQHaIHAO1RTQhO6sIwm9HZBEEQiwkJQwNCGPLlqpFKkh2iB5gihrEMwgG/p2iDIAhiKUDC0EBITyVlC2Xki8J89uYxAMDB4STNOiII4qKEhKGBuN6Qli6UjSmpXsZadJnGWFAvAkEQFyMkDA1ETcIghuHFPWxSawkH0BXXIoVVJAwEQVyEkDA0ENWnoWYKZWN8ttd5R+26z7CqjYSBIIiLDxKGBmJGxFBBulhGUPEh4Pf2a/rI9n6s7YjgnmtXLsQtEgRBLChzEgbG2EcYYwcYY1XG2PaGj32eMXacMXaEMfZe0/XrGWP79I99hTHG9OtBxth39euvMcbWzuXeZouIDkTE4HUIHgB8+tb1eP6PbsfK1vB83x5BEMSCM9eIYT+AXwHwovkiY2wLgPsAXAngLgBfY4yJ0p6vA7gfwCb9z1369U8BmOKcbwTwZQBfnOO9zYpYg8cQ8+AvEARBXArMSRg454c450csPnQPgEc55wXO+SkAxwHsYIz1Akhwzl/hnHMA3wZwr+nMI/rbjwO4Q0QTF5Kg4oPiY0gXykjPYtEOQRDExc5CeQx9AAZM7w/q1/r0txuv153hnJcBzADosPrijLH7GWO7GGO7xsbG5vXGGWOI6us5U3mKGAiCWH64CgNj7BnG2H6LP/c4HbO4xh2uO51pvsj5Q5zz7Zzz7V1dXc4/wCyIBRWk89qyndl4DARBEBczrk89zvmds/i6gwBWmd7vBzCkX++3uG4+M8gYUwC0AJicxfeeM62RAKZzJUxlSrisO74Yt0AQBLFoLFQq6QkA9+mVRuugmcyvc86HAaQYYzfq/sHHAfzAdOYT+tu/BuA53Ye44LRHVUykC5jIFIwRFwRBEMuFuZarfpgxNgjgJgBPMsZ+AgCc8wMAHgNwEMDTAB7gnFf0Y78H4GFohvQJAD/Wr38DQAdj7DiA/wjgc3O5t7nQGQtiYCqHfKmKjhjNOyIIYnkxpwQ65/z7AL5v87EHATxocX0XgK0W1/MAPjKX+5kvOqIqJjNF422CIIjlBHU+W9BuSh9RKokgiOUGCYMFndFa+qg9SqkkgiCWFyQMFmzsiRlvb+iKLuKdEARBXHhIGCy4qq/FeDseotWcBEEsL6h7y4KA34cv/upV6E6E3D+ZIAjiEoOEwYZfv2H1Yt8CQRDEokCpJIIgCKIOEgaCIAiiDhIGgiAIog4SBoIgCKIOEgaCIAiiDhIGgiAIog4SBoIgCKIOEgaCIAiiDrZIu3DmDcbYGIAzszzeCWB8Hm9nMaGfZWlCP8vS41L5OYC5/SxrOOeWu5EvemGYC4yxXZzz7Yt9H/MB/SxLE/pZlh6Xys8BLNzPQqkkgiAIog4SBoIgCKKO5S4MDy32Dcwj9LMsTehnWXpcKj8HsEA/y7L2GAiCIIhmlnvEQBAEQTRAwkAQBEHUsWyFgTF2F2PsCGPsOGPsc4t9P7OFMfZNxtgoY2z/Yt/LXGCMrWKM/ZwxdogxdoAx9tnFvqfZwhgLMcZeZ4zt1X+WP1vse5orjDE/Y+wNxtiPFvte5gJj7DRjbB9j7E3G2K7Fvp+5wBhrZYw9zhg7rP+7uWnevvZy9BgYY34ARwG8G8AggJ0AfoNzfnBRb2wWMMbeASAN4Nuc862LfT+zhTHWC6CXc76HMRYHsBvAvRfpfxMGIMo5TzPGAgB+AeCznPNXF/nWZg1j7D8C2A4gwTn/wGLfz2xhjJ0GsJ1zftE3uDHGHgHwEuf8YcaYCiDCOZ+ej6+9XCOGHQCOc85Pcs6LAB4FcM8i39Os4Jy/CGByse9jrnDOhznne/S3UwAOAehb3LuaHVwjrb8b0P9ctK/AGGP9AN4P4OHFvhdCgzGWAPAOAN8AAM55cb5EAVi+wtAHYMD0/iAu0ofQpQhjbC2AbQBeW+RbmTV66uVNAKMAfsY5v2h/FgB/A+CPAVQX+T7mAw7gp4yx3Yyx+xf7ZubAegBjAP5eT/E9zBiLztcXX67CwCyuXbSv6C4lGGMxAN8D8Iec8+Ri389s4ZxXOOfXAugHsIMxdlGm+RhjHwAwyjnfvdj3Mk/czDm/DsDdAB7QU7EXIwqA6wB8nXO+DUAGwLx5pctVGAYBrDK93w9gaJHuhdDR8/HfA/BPnPN/Xez7mQ/08P55AHct7p3MmpsBfEjPzT8K4F2MsX9c3FuaPZzzIf3vUQDfh5ZWvhgZBDBoikQfhyYU88JyFYadADYxxtbpps19AJ5Y5Hta1uiG7TcAHOKcf2mx72cuMMa6GGOt+tthAHcCOLyoNzVLOOef55z3c87XQvt38hzn/LcW+bZmBWMsqhc2QE+7vAfARVnNxzkfATDAGNusX7oDwLwVaijz9YUuJjjnZcbY7wP4CQA/gG9yzg8s8m3NCsbYPwO4DUAnY2wQwJ9wzr+xuHc1K24G8DEA+/TcPAD8Z875U4t3S7OmF8AjevWbD8BjnPOLuszzEqEHwPe11yBQAHyHc/704t7SnPgPAP5Jf3F7EsAn5+sLL8tyVYIgCMKe5ZpKIgiCIGwgYSAIgiDqIGEgCIIg6iBhIAiCIOogYSAIgiDqIGEgCIIg6iBhIAiCIOr4/wEitz2fWXszwAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,qian(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0360cdcf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x171e515b2b0>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,di(t),'r-')\n",
    "plt.plot(t,qian(t),'b-')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b16c93e3",
   "metadata": {},
   "source": [
    "### 3.后向差分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3beb144d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def hou(x):\n",
    "    h = 1e-5\n",
    "    return (f(x) - f(x - h)) / h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8956a8e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x171e51ba7c0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,hou(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2868b574",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x171e522f1c0>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,di(t),'r-')\n",
    "plt.plot(t,hou(t),'b-')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "243b0a17",
   "metadata": {},
   "source": [
    "### 4.中心差分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7ec63385",
   "metadata": {},
   "outputs": [],
   "source": [
    "def zhong(x):\n",
    "    h = 1e-5\n",
    "    return (f(x + h) - f(x - h)) / (2 * h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "84d79785",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x171e52904c0>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,zhong(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "73263c57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x171e52ecfa0>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,di(t),'r-')\n",
    "plt.plot(t,zhong(t),'b-')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4cc2559",
   "metadata": {},
   "source": [
    "### 5.龙贝格积分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "fe230867",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 -1.0651384978069502e-13\n",
      "1 -3.255440405020227e-07\n",
      "2 -2.463025588439851e-05\n",
      "3 -0.0001642258535416358\n",
      "4 -0.00044609238018299976\n",
      "5 0.003734168183105377\n",
      "6 0.0027540416962158593\n",
      "7 0.0005536724744676774\n",
      "8 -0.00265764476853737\n",
      "9 -0.002064206072133351\n",
      "10 -0.0016031345883026206\n",
      "11 -0.015466240055868889\n",
      "12 0.028579857503323883\n",
      "13 -0.032084912830070506\n",
      "14 0.0326524232867941\n",
      "15 -0.038536475707901884\n",
      "16 -0.009028597520245358\n",
      "17 -0.02863591825134511\n",
      "18 -0.01057261973157537\n",
      "19 0.0017207094300684509\n",
      "20 -0.03825724328090794\n",
      "21 0.04780537585689451\n",
      "22 0.01830775983295468\n",
      "23 -0.05220054731453743\n",
      "24 -0.02610644997825314\n",
      "25 0.05716581578985248\n",
      "26 -0.060834819118037314\n",
      "27 -0.02972159766973484\n",
      "28 0.06039300830837246\n",
      "29 -0.038539438354182456\n",
      "30 0.02039587506069276\n",
      "31 0.013344559435959745\n",
      "32 -0.006660840878028425\n",
      "33 -0.043278551733808915\n",
      "34 0.04425201689150704\n",
      "35 -0.06005933820758618\n",
      "36 0.0029944357456652237\n",
      "37 0.00745239457088435\n",
      "38 0.006616943433213118\n",
      "39 -0.0019427486213373013\n",
      "40 -0.017840414558205727\n",
      "41 -0.04470601856964534\n",
      "42 0.05081621814429125\n",
      "43 -0.0268712768715674\n",
      "44 0.056660778058446826\n",
      "45 -0.03307075093974478\n",
      "46 0.0354226111459608\n",
      "47 -0.06164157359517121\n",
      "48 0.005011097108954165\n",
      "49 0.013375615895605658\n",
      "50 0.029963182456267053\n",
      "51 0.04019743521602256\n",
      "52 -0.04251479939756273\n",
      "53 -0.04238625468473294\n",
      "54 -0.035077508471778526\n",
      "55 -0.036271885771028065\n",
      "56 -0.009961886290937005\n",
      "57 0.05926123070908136\n",
      "58 0.01771098923092073\n",
      "59 0.004412458807280967\n",
      "60 -0.004590464712593464\n",
      "61 -0.01795735854338224\n",
      "62 -0.04678271868513693\n",
      "63 0.05063978440170454\n",
      "64 -0.009087450439143836\n",
      "65 -0.023478715635660372\n",
      "66 0.0610735443879535\n",
      "67 -0.01142906994554789\n",
      "68 -0.02483859286667149\n",
      "69 0.04812185015479517\n",
      "70 -0.016114608281571935\n",
      "71 -0.05168695298636669\n",
      "72 0.02731960096306469\n",
      "73 -0.033019182016192986\n",
      "74 0.028633072953087105\n",
      "75 -0.025234969518362356\n",
      "76 0.030578704127485024\n",
      "77 -0.024405963432693283\n",
      "78 0.028456936819515322\n",
      "79 -0.026841211242769492\n",
      "80 0.022690500782231286\n",
      "81 -0.03521104687615805\n",
      "82 0.01761078260628419\n",
      "83 -0.05683484956554454\n",
      "84 0.0165020127505775\n",
      "85 0.04057037774011623\n",
      "86 -0.027810833636823053\n",
      "87 0.01741443178693417\n",
      "88 -0.05608254829596451\n",
      "89 0.014550223608489676\n",
      "90 0.025333745469711014\n",
      "91 -0.03498866342251062\n",
      "92 0.010993814218989236\n",
      "93 0.03498785551797601\n",
      "94 -0.032635798376720544\n",
      "95 0.010032627490322174\n",
      "96 0.032578247099726704\n",
      "97 -0.034861909379031386\n",
      "98 0.008501350527249835\n",
      "99 0.02118558436352528\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "def trapezoidal(f, n, a, b):\n",
    "    xArr = np.linspace(a, b, n + 1)\n",
    "    return (b - a) / n * (np.sum(f(xArr)) -   1 / 2 * (f(a) + f(b)))\n",
    "def simpson(f, a, b):\n",
    "    h = (b - a) / 2\n",
    "    return h / 3 * (f(a) + f(b) + 4 * (f((a + b) / 2))) \n",
    "def f(p):\n",
    "    return 2*12*np.sin(d*p/(2*L))*np.exp(-(0.1)*p/(2*L))*(1/d)\n",
    "def fInt(a, b):\n",
    "    return 2\n",
    "n = 100\n",
    "R = np.zeros((n, n))\n",
    "X = np.zeros(n)\n",
    "a = 0\n",
    "b = 6\n",
    "for i in range(n):\n",
    "    R[i, 0] = trapezoidal(f, i + 1, a, b)\n",
    "    for j in range(1, i + 1):\n",
    "        R[i, j] = (4 ** j * R[i, j - 1] - R[i - 1, j - 1]) / (4 ** j - 1)\n",
    "    X[i] = R[i,i]\n",
    "    print(i, R[i,i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b5179700",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "积分结果为：0.0001197936\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "a=0             \n",
    "b=3            \n",
    "eps=1e-5     \n",
    "T=[]           \n",
    "S=[]            \n",
    "C=[]            \n",
    "R=[]            \n",
    "def func(x):  \n",
    "    return 2*E*np.sin(d*x/(2*L))*np.exp(- 0.1 *x/(2*L))*(1/d)\n",
    "def Romberg(a,b,eps,func):\n",
    "    h = b - a\n",
    "    T.append(h * (func(a) + func(b)) / 2)\n",
    "    ep=eps+1\n",
    "    m=0\n",
    "    while(ep>=eps):\n",
    "        m=m+1\n",
    "        t=0\n",
    "        for i in range(2**(m-1)-1):\n",
    "            t=t+func(a+(2*(i+1)-1)*h/2**m)*h/2**m\n",
    "        t=t+T[-1]/2\n",
    "        T.append(t)\n",
    "        if m>=1:\n",
    "            S.append((4**m*T[-1]-T[-2])/(4**m-1))\n",
    "        if m>=2:\n",
    "            C.append((4**m*S[-1]-S[-2])/(4**m-1))\n",
    "        if m>=3:\n",
    "            R.append((4**m*C[-1]-C[-2])/(4**m-1))\n",
    "        if m>4:\n",
    "            ep=abs(10*(R[-1]-R[-2]))\n",
    "Romberg(a,b,eps,func)\n",
    "print(\"积分结果为：{:.10f}\".format(R[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5551a91d",
   "metadata": {},
   "source": [
    "### 6.高斯积分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a19788f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(p):\n",
    "    return 2*E*np.sin(d*p/(2*L))*np.exp(-(0.1)*p/(2*L))*(1/d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "23289790",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10000\n",
    "tiList,CiList = np.polynomial.legendre.leggauss(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6df166d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 0\n",
    "b = 3\n",
    "xiList = (b-a)/2 *(tiList-1)+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1e3eee39",
   "metadata": {},
   "outputs": [],
   "source": [
    "(b-a)/2 *CiList.dot(f(xiList))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59ec94f2",
   "metadata": {},
   "source": [
    "上面龙贝格积分看同学的还能有一部分看懂，这个高斯积分确实不明白。。。就不跑了也。。。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66fc7f75",
   "metadata": {},
   "source": [
    "### 7.心得体会"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7d720dd",
   "metadata": {},
   "source": [
    "不要翘课。。不要翘课。。不要翘课。。无论起不来或是参加活动被迫。。。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "273cdac8",
   "metadata": {},
   "source": [
    "这次项目微分部分还好，积分部分可以说就是不会。。。梯形积分和辛普森积分还好一点，要编的这两个积分可以说确实不会。。"
   ]
  }
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